Thyreophagus (Acari: Acaridae) are distributed worldwide; they inhabit concealed habitats and include several beneficial and economically important species. However, species identification is difficult because many species are poorly described or delimited and their phoretic stages are unknown or uncorrelated. Furthermore, Thyreophagus is interesting because it includes entirely asexual (parthenogenetic) species. However, among the 34 described species of Thyreophagus, the asexual status is confirmed through laboratory rearing for only two species. Here, we provide detailed descriptions of five new species from North America (four) and Europe (one) based on adults and phoretic heteromorphic deutonymphs. Four of these species were asexual, while one was sexual. For most of these mites, the asexual status was confirmed and phoretic deutonymphs were obtained through rearing in the lab. We show that asexual mites retain seemingly functional copulatory and sperm storage systems, indicating that these lineages have relatively short evolutionary lifespans. One North American species, Thyreophagus ojibwe, was found in association with the native American chestnut Castanea dentata, suggesting a possibility that this mite can be used to control chestnut blight in North America. We also provide a diagnostic key to females, males, and heteromorphic deutonymphs of the Thyreophagus species in the world.Mites of the genus  Thyreophagus  is distributed worldwide, except in Antarctica [Thyreophagus corticalis  is beneficial because it is a natural vector of a hypovirus pathogenic to the ascomycete fungus Cryphonectria parasitica that causes chestnut blight, a dangerous disease of chestnuts in temperate regions in the northern hemisphere [C. parasitica and reduces its parasitic growth, leading to the spontaneous recovery of infected chestnut trees, Castanea sativa, from the disease in Europe [C. parasitica was inadvertently introduced to North America, it caused the functional extinction of the American chestnut Castanea dentata [The genus Rondani, 874 is ditarctica ,3,4,5. TRondani, 874 is ditarctica ,6,7,8,9.tarctica ,11,12. Tmisphere . The hypn Europe ,15. When dentata . Efforts dentata .Thyreophagus live in concealed habitats, they have been generally overlooked and understudied by researchers in comparison to most other acarid mite genera. The lack of correlation of adult and deutonymphal stages for many species; the presence of old, insufficiently described, unrecognizable taxa; the lack of types; and unclear species boundaries are cited as being the major impediments to the systematics of Thyreophagus [Th. Australis , Th. Corticalis, Th. Entomophagus, and Th. Calusorum Klimov, Demard, Stinson, Duarte, Wäckers, and Vangansbeke, 2022 [Thyreophagus is the presence of both sexual and asexual species, although only a few species from the latter group are known to date: Th. Calusorum, Th. Plocepasseri , and an unnamed species from a wasp nest in Japan [Since most species of eophagus . As an eke, 2022 ,18,19,20Castanea dentata, thus opening avenues for further research investigating whether the mite also can vector a hypoviruses that can infect and control the fungal pathogen of the tree. We demonstrate that females of asexual species retain functional structures responsible for insemination and sperm storage, with no signs of morphological reductions observed in the spermatheca. This suggests that these taxa are recent and probably evolutionary short-lived asexuals, thus meriting further genomic research into the potential causes of their asexual mode of reproduction. We also provide a diagnostic key to females, males, and heteromorphic deutonymphs for all known Thyreophagus species in the world.Here, we provide detailed descriptions of five new species from North America (four) and Europe (one) based on adult and phoretic heteromorphic deutonymphs. Four of these species were asexual, while one was sexual. The asexual status for most of these mites was confirmed through lab rearing. One North American species was found in association with the native American chestnut Fallen tree branches were collected from forest litter and processed in the lab. Feeding stages of live mites were sampled in subcortical spaces under a Zeiss Stemi DV4 dissecting microscope. Voucher specimens were mounted on slides, preserved in ethanol, or cultured  using bran as a food source, with the addition of baker’s yeast . The culture was harvested and subcultured several times to obtain a large number of specimens and heteromorphic deutonymphs. The specimens were preserved in ethanol, cleared in Nesbitt’s fluid for 1–2 days, mounted in Hoyer’s medium, and dried at 60 °C for 7 days . To contImages were taken using a Nikon Eclipse E800 microscope equipped with a DIC optic and a Tucsen Discovery CH30 digital camera, and a Zeiss Axio Imager.A2 equipped with a DIC optic and Axiocam 305 color camera. Images were taken from multiple focal planes and assembled in Helicon Focus 7.6.4 Pro  with subsequent manual editing to add missing fine detail from the individual focal planes (retouching). Parts of the layered images were combined in Adobe Photoshop 22.2.0. Line drawings were created in Photoshop using microphotographs as the background.The idiosomal chaetotaxy followed Griffiths et al. ; the terThyreophagus ais Klimov, Kolesnikov, Demard, Vangansbeke sp. n..urn:lsid:zoobank.org:pub:7C7FEAA7-EB57-4A12-A489-196D2BEEA5D9.Type material. Holotype: One female—lab culture on bran, harvested 26 February 2021, culture started from specimens originated from the USA, Florida, Fort Pierce, branches on ground in a small wooded area, subcortical, 27°25′34.5″ N 80°24′22.7″ W, 20 November 2020, Emilie Demard coll., BMOC 20-0101-014#S1.1. Paratypes: 3f , 6 HDNs —same data; 2f—original wild sample (see above).Depository. Holotype, paratypes—University of Michigan, Museum of Zoology, Ann Arbor, Michigan, USA.Etymology. The new species is named after the Ais people who lived in the eastern coastal area of central Florida  but went extinct after the arrival of European colonizers [lonizers .Habitat. Thyreophagus ais lives under the bark of small fallen branches of deciduous trees in wooded areas. These branches are typically in the initial stages of decomposition, with approximately 80% of their natural sapwood retaining a white color, and 20% displaying brown discoloration, indicating the ongoing decomposition process. Additionally, the bark usually exhibits boreholes from wood-boring beetles.DescriptionFemale (n = 4), 2.4 -times longer than wide. Idiosomal cuticle smooth. Subcapitular setae (h) long, widened basally; palp tibial setae (a), lateral dorsal palp tibial setae (sup), dorsal palp tarsal seta (cm) filiform; supracoxal seta elcp absent; terminal palp tarsal solenidion ω short; external part of eupathidium ul’’ dome-shaped; terminal eupathidium ul’ not observed. Prodorsal sclerite 105  long, 96  wide, 1.1 -times longer than wide, both smoothly punctated and very finely longitudinally striated, except in anterior 1/5 (smoothly punctate) and posterior 1/4 (ornamented with distinct pattern of broken striae arranged in a triangle). Prodorsal sclerite with setae vi situated at anterior part of shield (bases touching but separated from each other), rounded anterolateral incisions, and elongate midlateral incisions (corresponding to insertion points of setae ve).Female . Idiosomscx) smooth, sword-shaped, widened, and flattened, tapering at tip. Idiosomal setae  smooth, filiform, and short; opisthosomal gland openings slightly anteriad of setal bases e2. One pair of fundamental cupules (ia) present (other cupules not observed).Grandjean’s organ (GO) expanded into 13 membranous finger-like extensions. Supracoxal seta  and one pair of genital setae (g). Shape of coxal sclerites as shown in Ventral idiosoma with four pairs of coxal setae ; s flattened, button-shaped; setae wa absent. Tarsal II setation similar to that of tarsus I, except proral setae  represented by small triangular rudiments  of tarsus I wide, spiniform, with broadly rounded apex, widest at middle. Solenidia φ of tibiae I–III elongate, tapering, well-extended beyond apices of respective tarsi with ambulacra; solenidion φ IV shorter, shorter than tarsus IV (with ambulacra). On genu I, solenidion σ’ elongate, tapering, slightly not reaching bases of φ I, about 1.8-times longer than σ’’; σ’’ I slightly wider than σ’, about half the length of tibia I. On genu II, solenidion σ very short and somewhat conical. Solenidion σ of genu III absent.Legs short. Trochanters I–III each with long, filiform seta, udiments J. TarsusMale. Absent.Heteromorphic deutonymph (n = 4), widest in sejugal region; idiosomal length 210–240, n = 4 width 130–150, n = 4. Gnathosoma short, subcapitulum and palp fused, bearing apical palpal solenidia (ω) and filiform apicodorsal setae (sup); setae h absent from subcapitular remnant, their positions marked by refractile spots.utonymph . Body elvi) (bases separated) and a single sclerite. A pair of lateral ocelli present on propodosoma, widely separated from each other ; lenses and pigmented spots present; maximal diameter of lenses 12–14, n = 4. External vertical setae (ve) absent; external scapular setae se situated just below eye lenses; internal scapular setae (si) distinctly posterior and medial to external scapulars (se). Supracoxal setae of legs I (scx) filiform, with extended base, satiated below se. Sejugal furrow well-developed. Propodosomal sclerite 65–80, n = 4, hysterosomal shield 139–160, n = 4, ratio hysterosomal shield/propodosomal sclerite = 2.0–2.13. Hysterosomal shield with 11 pairs of simple, filiform setae , setae h3 distinctly longer than others. Opisthonotal gland openings (gla) ventral, situated on hysterosomal shield, slightly posterior to setae c3. Of four fundamental pairs of cupules, three pairs observed: ia posteriomediad of setae c2, im ventral, lateral to trochanter IV, ih ventral, lateral to posterior portion of attachment organ.Dorsum. Propodosoma and hysterosoma each covered by smoothly punctate shields; distinct linear pattern present on anterior and lateral sides of propodosomal sclerite and hysterosomal shield. Anterior propodosoma with internal vertical setae (c3) filiform, situated on ventral surface between legs II–III, adjacent to region separating sternal and ventral shields. Coxal setae 1a, 3a reduced, represented by very small structures each within an alveolus. Coxal setae (4b) filiform, situated at tips anterior to coxal apodemes IV; 4a in form of small, rounded conoids. Progenital region in posterior portion of coxal fields IV; genital opening elongate; two pairs of genital papillae within genital atrium; genital papillae two-segmented, with rounded apices; genital setae (g) filiform, situated laterad of genital opening. Attachment organ posterior to coxal fields IV. Anterior suckers (ad3) round, median suckers (ad1+2) distinctly larger, with paired vestigial alveoli; pair of small refractile spots anterolateral to median suckers (ps3); lateral conoidal setae of attachment organ (ps2) situated distinctly posterior to line joining centers of median suckers, slightly anterior conoids (ps1) and slightly posterior to median suckers (ad1+2); anterior and posterior lateral and posterior median cuticular conoids well-developed; anus situated between anterior suckers (ad3).Venter. Coxal fields sclerotized, smoothly punctate. Anterior apodemes of coxal fields I fused forming sternum; sternum not reaching posterior border of sternal shield by distance exceeding its length. Posterior border of sternal shield not sclerotized. Anterior apodemes of coxal fields II curved medially. Posterior apodemes of coxal fields II weakly developed, thin. Sternal and ventral shield adjacent. Anterior apodemes of coxal fields III free, connected by thin transverse sclerotization. Posterior medial apodeme present in area of coxal fields IV, well-separated from anterior apodemes IV and genital opening. Posterior apodemes IV absent. Subhumeral setae , setae d elongate, their bases situated at level anterior to bases of setae ra and la; one spoon-shaped seta e; setae s alveolar, setae wa, aa and ba I absent; tarsus II similar to tarsus I except seta ba present and filiform, close to ω1. Tarsus III with eight setae  smooth; all setae, except d III more or less foliate; seta d equal to or longer than leg III. Tarsus IV similar to tarsus III, except setae q and p short, spiniform, seta r longer, filiform, seta w filiform and with distinct prong, seta d distinctly longer than legs IV. Solenidia ω1 on tarsi I–II cylindrical, with slightly clavate apices; ω3 on tarsus I slightly shorter than ω1, with rounded apex, positioned slightly anterior to ω1; ω1 and ω3 separated by bulbous famulus (ε); solenidion ω2 of tarsus I slightly widened apically, situated somewhat more basal and posterior to ω1 + ε+ω3 group; solenidia φ of tibiae I–III elongate, tapering; φ I longer than tarsus I; φ II shorter than tarsus II; φ III reaching tip of tarsus III without ambulacrum; φ IV short; σ of genu I elongate, tapering slightly, nearly reaching tip of tibia I; σ of genu II shorter, cylindrical, not reaching midlength of tibia II; σ of genu III absent.Legs. Legs elongate, all segments free. Trochanters I–III each with long, filiform seta, filiform B; setae DiagnosisThyreophagus ais is close to Th. calusorum, Th. mauritianus , Th. gallegoi Portus and Gomez, 1979 and Th. vermicularis Fain and Lukoschus, 1982 in having a very short solenidion σ II. Th. ais is similar to Th. calusorum and Th. mauritianus by the shape of solenidion σ II, which has convex sides , but it differs from Th. calusorum by the following: sclerites of oviducts are Y-shaped ; the canal of spermatheca at the entrance to spermatheca is not widened . Th. ais differs from Th. mauritianus as follows: the cuplike portions of the sclerites of oviducts are subequal to their stems (Th. mauritianus [Th. mauritianus); solenidion ω1 II is three-times longer than its width (five-times longer in Th. mauritianus); and solenidion φ IV is nearly reaching the bases of setae d IV (reaching the middle of tarsus IV in Th. mauritianus). Th. ais differs from Th. gallegoi by the absence of linear sclerites near the typical sclerites of oviducts  and from Th. vermicularis by the Y-shaped paired sclerites of oviducts, which are at least three-times longer than their width .Female.  widened I vs. wid Fain, 192, Th. ga Fain, 192, Th. ga Fain, 192, Th. gaTh. ais is very similar to Th. calusorum, but differs by short, spiniform setae q and p IV , setae d III are longer than leg III , d IV distinctly longer than leg IV . Setae hT I and kT IV are always spiniform in Th. ais, but it can be variable, either spiniform or filiform in Th. calusorum .Heteromorphic deutonymph. Thyreophagus hobe Klimov, Kolesnikov, Demard, Vangansbeke, sp. n..urn:lsid:zoobank.org:pub:7C7FEAA7-EB57-4A12-A489-196D2BEEA5D9.Type material. Holotype: female—USA: Florida, Fort Pierce, branches on ground in a small, wooded area, subcortical, stick3, 27°25′34.5″ N 80°24′22.7″ W, 12 October 2020, Emilie Demard, BMOC 20-0101-008. Culture maintained until 26 February 2021 but then was accidentally lost (no specimens from these cultures were preserved).Depository. Holotype—University of Michigan, Museum of Zoology, Ann Arbor, Michigan, USA.Etymology. The new species is named after the Hobe Indians who lived in the eastern coastal area of central Florida (between St. Lucie and Jupiter inlets), but went extinct after the arrival of European colonizers [6, which is reminiscent of the long dorsal setae of Thyreophagus hobe.lonizers . The menHabitat. Thyreophagus hobe lives under the bark of small fallen branches found in wooded areas. These branches are typically in the initial stages of decomposition, with approximately 80% of their natural sapwood retaining a white color, and 20% displaying brown discoloration, indicating the ongoing decomposition process.DescriptionFemale (h) long, widened basally; palp tibial setae (a), lateral dorsal palp tibial setae (sup), dorsal palp tarsal seta (cm) filiform; supracoxal seta elcp present, slightly widened basally; terminal palp tarsal solenidion ω short; external part of terminal eupathidium ul’’ dome-shaped; terminal eupathidium ul’ not observed. Prodorsal sclerite 63 long, 46 wide, 1.4-times longer than wide, with setae vi , rounded anterolateral incisions, and elongate midlateral incisions (corresponding to insertion points of setae ve); shield punctate, 3/4 of posterior central region with linear pattern. Grandjean’s organ (GO) expanded anteriorly into membranous finger-shaped extensions (exact number cannot be observed on the single specimen). Supracoxal seta (scx) smooth, sword-shaped, widened and flattened, tapering at tip. Idiosomal setae  smooth, filiform, setae h2 and h3 very long ; opisthosomal gland openings slightly anteriad of setal bases e2. Four pairs of fundamental cupules  present.Female . Idiosom1a, 3a, 4a, and 4b) and one pair of genital setae (g), seta 4b unpaired in holotype . Shape of coxal sclerites as shown in Ventral surface of idiosoma with four pairs of coxal setae , setae wa absent. Tarsus II setation similar to that of tarsus I. Tarsus III with eight setae; f, d, r filiform; e and s spiniform; p, q, u, and v similar to these of tarsus I–II; seta w flattened, button-shaped. Tarsus IV similar to tarsus III, except w filiform. Solenidion ω1 on tarsus I cylindrical, with clavate apex, slightly curved; solenidion ω1 on tarsus II simple, cylindrical, with clavate apex, not bent, longer than ω1 on tarsus I. Solenidion ω2 on tarsus I shorter than ω1, cylindrical, with rounded apex, slightly expanded at tip, situated slightly anterior and external to ω1. Solenidion ω3 on tarsus I cylindrical, with rounded apex, shorter than ω1 I. Famulus (ε) of tarsus I spiniform, with pointed apex. Solenidia φ of tibiae I–III elongate, tapering, well extending beyond apices of respective tarsi with ambulacra; solenidion φ IV shorter than tarsus IV (with ambulacra). Genual solenidia σ’ and σ’’ I elongate, tapering, subequal, slightly not reaching bases of φ I. Genual solenidion σ II 7–9-times longer than its width, with rounded tip. Genual solenidion σ III absent.Legs short, all segments free. Trochanters I–III each with long, filiform seta, Male. Absent.Heteromorphic deutonymph. Unknown.DiagnosisThyreophagus hobe differs from all known species of Thyreophagus by the absence of femoral setae wF IV and unguinal setae u, v I–IV. Like Th. australis Clark, 2009, Th. hobe has very long setae h2 and h3 , but in Th. hobe, setae h1 five-times shorter than h2 and h3 .Female. Thyreophagus ojibwe Klimov, Kolesnikov, Vangansbeke, sp. n..urn:lsid:zoobank.org:pub:7C7FEAA7-EB57-4A12-A489-196D2BEEA5D9.Type material. Holotype female (f1), paratype female (f2)—USA: Michigan, Michigan State University Chestnut Plantation, Castanea dentata , branch on ground (tree1.stick1), 42°09′06.6″ N 84°25′33.2″ W, 23 November 2020, P. Klimov, BMOC 20-0101-010#slide1; 1 paratype female—same data, slide 2; 1 paratype female—same data, C. dentata blight tissues, BMOC 20-0101-012#slide3.Non-type material. One male, two females—CANADA: Ontario C.E.F., Ottawa, under bark of dead willow twigs, Salix sp. , O. Peck, 1974 CNC788949  ).Depository. Holotype, paratypes—University of Michigan, Museum of Zoology, Ann Arbor, Michigan, USA.Etymology. The new species is named after the Ojibwe, North American indigenous people from what is currently southern Canada and Midwestern United States, including the state of Michigan.Habitat. Thyreophagus ojibwe lives under the bark of small fallen branches typically found around American chestnut trees. These branches are generally in the initial stages of decomposition. Additionally, mites were found on the blight-infected tissues, suggesting that these mites can likely feed on this harmful fungus and potentially transmit hypoviruses.DescriptionFemale (n = 3), 2.3 -times longer than wide. Idiosomal cuticle smooth. Subcapitular setae (h) long, widened basally; palp tibial setae (a), lateral dorsal palp tibial setae (sup), dorsal palp tarsal seta (cm) filiform; supracoxal seta elcp present, slightly widened basally; terminal palp tarsal solenidion ω short; external part of terminal eupathidium ul’’ dome-shaped; terminal eupathidium ul’ not observed. Prodorsal sclerite 85  long, 75  wide, 1.1 -times longer than wide, with setae vi , rounded anterolateral incisions, and elongate midlateral incisions (corresponding to insertion points of setae ve); shield smoothly punctate, 3/4 of posterior central region with linear pattern. Grandjean’s organ (GO) with 8 membranous, finger-shaped extensions. Supracoxal seta (scx) smooth, sword-shaped, widened and flattened, tapering at tip. Idiosomal setae  smooth, filiform; setae h2 and h3 long, 1.75-times longer than length of prodorsal sclerite; opisthosomal gland openings slightly anteriad of setal bases of e2. Four pairs of fundamental cupules  present.Female . Idiosom1a, 3a, 4a, and 4b) and one pair of genital setae (g). Shape of coxal sclerites as shown in Ventral surface of idiosoma with four pairs of coxal setae . Solenidion ω2 on tarsus I shorter than ω1, cylindrical, with rounded apex, slightly widened at tip, situated slightly anterior and external to ω1. Solenidion ω3 on tarsus I cylindrical, with rounded apex, shorter than ω1, longer than ω2. Famulus (ε) of tarsus I wide, spiniform, with broadly rounded apex, widest at middle. Solenidia φ of tibiae I–III elongate, tapering, well extending beyond apices of respective tarsi with ambulacra; solenidion φ IV shorter, almost reaching tip of tarsus IV (without ambulacra). Genual solenidia σ’ and σ’’ I elongate, tapering, subequal, slightly not reaching bases of φ I. Genual solenidion σ II 10-times longer than its width) and somewhat conical. Genual solenidion σ III absent.Legs short, all segments free. Trochanters I–III each with long, filiform seta, Male (n = 1)  . Idiosomscx) as in female. Idiosomal setae  smooth, filiform, setae h2 and h3 long ; opisthosomal gland openings slightly anteriad of setal bases e2. Four pairs of fundamental cupules  present. Opisthonotal shield solid, whole, smoothly punctated; ventral part of shield extends to anal suckers.Grandjean’s organ (GO) and supracoxal seta  and one pair of genital setae (g). Shape of coxal sclerites shown in ps1-3 very short.Ventral surface of idiosoma with four pairs of coxal setae ; the diameter of the genital papillae is approximately four-times shorter than the length of genital setae ; the stem of the Y-shaped sclerites of oviducts is about 3–4-times shorter than the length of Y-shaped sclerites of oviducts ; ventral apical spines p and q of tarsi III–IV are shorter than spines u and v III–IV .Female. Th. ojibwe differs from Th. corticalis by the longer setae h2 and h3  and by spines p and q on tarsi III–IV, which are shorter than spines u and v .Male. Thyreophagus potawatomorum Klimov, Kolesnikov, Vangansbeke, sp. n..urn:lsid:zoobank.org:pub:7C7FEAA7-EB57-4A12-A489-196D2BEEA5D9.Type material. Holotype female (f2) and one paratype female (f1)—USA: Michigan, Ann Arbor, Hansen Nature Area, stick 5, 42°16′03.8″ N 83°46′53.2″ W, 14 October 2020, P. Klimov, BMOC 20-0101-004#slide 1; four paratype females—same data , slide 2; six paratype females—same data, slide 3; two paratype HDNs—same data, slide 5; one paratype HDN—same data, slide 6; one paratype HDN—same data, slide 8.Non-type material. Two DNs, one pharate DN—same data, slide 7.Depository. Holotype, paratypes—University of Michigan, Museum of Zoology, Ann Arbor, Michigan, USA.Etymology. This species is named after Potawatomi, native American people of the Great Plains, upper Mississippi River, and western Great Lakes region (including the state of Michigan).Habitat. Thyreophagus potawatomorum lives under the bark of small fallen branches of deciduous trees in wooded areas. These branches are typically in the initial stages of decomposition, with approximately 80% of their natural sapwood retaining a white color, and 20% displaying brown discoloration, indicating the ongoing decomposition process. Additionally, the bark usually exhibits boreholes from wood-boring beetles.DescriptionFemale (h) long, widened basally; palp tibial setae (a), lateral dorsal palp tibial setae (sup), dorsal palp tarsal seta (cm) filiform; supracoxal seta elcp present, widened basally; terminal palp tarsal solenidion ω short, bacilliform; external part of terminal eupathidium ul’’ dome-shaped; terminal eupathidium ul’ not observed. Prodorsal sclerite 88  long, 80  wide, 1.1 -times longer than wide, with setae vi , rounded anterolateral incisions, and elongate midlateral incisions (insertion points of setae ve). Prodorsal sclerite punctate, with longitudinal linear pattern extending anteriorly from posterior end of sclerite and covering area exceeding 75% of sclerite; anterior lateral and medial areas have only punctate patterns; lines form a triangle at posterior end of sclerite. Grandjean’s organ (GO) with seven membranous finger-like processes; central process distinctly wider than remaining processes. Supracoxal seta (scx) smooth, sword-shaped, widened and flattened, tapering at tip, slightly curved. Idiosomal setae  smooth, filiform, short and slender; opisthosomal gland openings slightly anteriad of setal bases e2. Four pairs of fundamental cupules  present.Female . Idiosom1a, 3a, 4a, and 4b) and one pair of genital setae (g). Shape of coxal sclerites as shown in Ventral idiosoma with four pairs of coxal setae  represented by small triangular rudiments. Tarsus III with 10 setae; f, d, r filiform; e, w, s, u, v, p, q spiniform. Tarsus IV similar to tarsus III, except w filiform. Solenidion ω1 on tarsus I cylindrical, with clavate apex, bent and pointed outward, to posterior side of tarsus; solenidion ω1 on tarsus II simple, cylindrical, with clavate apex, not bent, shorter than ω1 on tarsus I. Solenidion ω2 on tarsus I shorter than ω1, cylindrical, with rounded apex, slightly widened at tip, situated slightly anterior and external to ω1. Solenidion ω3 on tarsus I cylindrical, with rounded apex, shorter than ω1, longer than ω2. Famulus (ε) of tarsus I wide, spiniform, with broadly rounded apex. Solenidia φ of tibiae I–III elongate, tapering, well extending beyond apices of respective tarsi with ambulacra; solenidion φ IV shorter than tarsus IV (with ambulacra). On genu I, solenidion σ’ elongate, with rounded tip, slightly not reaching bases of φ I, about 1.5-times longer than σ’’; σ’’ I distinctly wider than σ’, about half the length of tibia I. On genu II, solenidion σ short (more than three-times longer than its width), with rounded tip. Solenidia σ III and IV absent.Legs short, all segments free. Trochanters I–III each with filiform seta, Male. Absent.Heteromorphic deutonymph (n = 1) ((sup); setae h absent from subcapitular remnant, their positions marked by somewhat refractile spots. (n = 1) . Body elvi), sitiated on apex of propodosoma, long, bases separated. A pair of lateral ocelli present on propodosoma; widely separated from each other ; lenses and pigmented spots present, maximal diameter of lenses 16. External vertical setae (ve) absent; external scapular setae se situated just below eye lenses; internal scapular setae (si) distinctly posterior and medial to external scapulars (se). Supracoxal setae of legs I (scx) filiform, situated below se. Sejugal furrow well-developed. Propodosomal sclerite 73, hysterosomal shield 160, ratio hysterosoma shield/propodosomal sclerite, length = 2.19. Hysterosoma with 11 pairs of simple, filiform setae on hysterosomal shield , setae h3 distinctly longer than others. Opisthonotal gland openings (gla) ventral; situated slightly posterior to setae 3c off hysterosomal shield. Of four fundamental pairs of cupules, only three pairs observed: ia posteriomedial of setae c2, im posterior of d2 level and ih ventral, lateral to posterior sides of attachment organ.Dorsum. Propodosomal and hysterosomal smoothly punctate; distinct linear pattern present on anterior and lateral sides of propodosomal sclerite and hysterosomal shield. Apex of propodosomal sclerite shaped as obtuse triangle. Internal vertical setae (c3) long, filiform, positioned on ventral surface between legs II–III, adjacent to region separating sternal and ventral shields. Coxal setae 1a, 3a reduced, represented by minute structures each situated in an alveolus. Setae 4b, g filiform; 4a in form of small, rounded conoids, 4b longer than g. Genital region in posterior portion of coxal fields IV; genital opening elongate, there are two pairs of genital papillae inside progenital atrium; papillae two-segmented, with rounded apices. Coxal setae (4b) situated at tips anterior to coxal apodemes IV; genital setae (g) situated laterad of genital opening. Attachment organ posterior to coxal fields IV. Anterior suckers (ad3) round, median suckers (ad1+2) distinctly larger, with paired vestigial alveoli; pair of small refractile spots anterolateral to median suckers (ps3); lateral conoidal setae of attachment organ (2ps) situated slightly posterior to a line joining centers of median suckers, distinctly anterior conoidal setae (ps1) and slightly posterior to median suckers (ad1+2); anterior and posterior lateral and posterior median cuticular conoids well-developed; anus positioned between anterior suckers (ad3).Venter. Coxal fields sclerotized, smoothly punctate. Anterior apodemes of coxal fields I fused forming sternum. Sternum not reaching posterior border of sternal shield by distance exceeding its length. Posterior border of sternal shield weakly sclerotized. Anterior apodemes of coxal fields II curved medially. Posterior apodemes of coxal fields II weakly developed, thin. Sternal and ventral shields adjacent. Anterior apodemes of coxal fields III free. Posterior medial apodeme present between coxal fields IV, well-separated from anterior apodemes IV and genital opening. Posterior apodemes IV absent. Dorsal hysterosomal shield separated from ventral surface by a distinct suture on each side. Subhumeral setae , three slightly foliate seate , and one spoon-shaped seta e. Seta d I elongate, longer than tarsus (its base situated at level of setae ra and la); seta s I alveolar; setae wa, aa and ba I absent. Tarsus II similar to tarsus I except seta ba present and filiform, base of seta d posterior to level of setae ra and la. Tarsus III with eight setae  smooth, all setae, except d III foliate. Tarsus IV similar to tarsus III, except seta r longer, filiform, and setae w filiform and has a distinct prong. Solenidia ω1 on tarsi I–II cylindrical, with slightly clavate apices, ω1 II longer than ω1 I. Solenidion ω3 on tarsus I slightly shorter than ω1, with rounded apex, positioned slightly anterior to ω1; famulus (ε) bulbous, situated between ω1 and ω3. Solenidion ω2 of tarsus I thin, with rounded apex, positioned somewhat more basal and posterior to ω1+ε+ ω3 group. Solenidia φ of tibiae I–III elongate, tapering; φ I and III, longer than tarsus I and III, respectively; φ II shorter than tarsus II; φ IV short. Solenidion σ of genu I elongate, slightly tapering, nearly reaching tip of tibia I; σ of genu II shorter, cylindrical, not reaching midlength of tibia II; σ of genu III absent.Legs. Legs elongate, all segments free. Trochanters I–III each with long, filiform seta, DiagnosisThyreophagus potawatomorum is similar to Th. spinitarsis  by the linear striations of the prodorsal sclerite extending over at least 75% of the sclerite length and by tarsi III having seven spiniform setae , but differs by the widened, vase-shaped atrium (dome-shaped in Th. spinitarsis). Th. potawatomorum is very close to Th. berxi sp. n., but differs by the following character states: setae vi are not extending beyond the anterior margin of the prodorsum (extending in Th. berxi); bases of vi touch each other (distinctly separated in Th. berxi), lines of the prodorsal sclerite are longer than the diameter of the bases of vi (shorter in Th. berxi); on the prodorsal sclerite, the anterior medial striated area differs from the posterior medial striated area ; opisthosomal setae h2 and h3 are shorter than the anus (distinctly longer in Th. berxi); a rounded capsule is present between the canal of spermatheca and the atrium (absent in Th. berxi).Females. Th. potawatomorum is close to Th. corticalis and Th. berxi by the following character states: body elongate (more than 1.7-times longer than wide), setae hT and gT I–II are present, different in shape, bases of setae d are at the level with bases of setae of ra and la on tarsus I. Th. potawatomorum differs from Th. corticalis and Th. berxi by the following character states: posterior median apodeme present, well-developed ; the diameter of ocelli is about 16 ; the distance between the ocelli is 36 ; setae wa I are absent ; on tibia IV, seta kT IV without distinct prong .Heteromorphic deutonymph. Thyreophagus berxi Klimov, Kolesnikov, Wäckers, Merckx, Duarte, Vangansbeke, sp. n..urn:lsid:zoobank.org:pub:7C7FEAA7-EB57-4A12-A489-196D2BEEA5D9.Type material. Holotype female, five paratype females—BELGIUM: East Flanders, Gentbrugge, Moscou, Fagus sylvatica  twig, subcortical, 51°01′50.7″ N 3°44′54.6″ E, 16 November 2019, Dominiek Vangansbeke, PBK 22-0905-033#slide1; one paratype female, same data, slide 2. One paratype female—BELGIUM: Flemish Brabant, Arenberg Castle, Leuven, Fagus sylvatica (label on slide = “19-1-20 Tr. Sp. LA Arenberg beech 1”), 50°51′32.6″ N 4°39′54.4″ E, 19 January 2020, Jonas Merckx, PBK 22-0905-034#slide1. Six paratype females, one paratype HDN—GERMANY: Saxony, Dresden, Betula  , 51°05’38.7″ N 13°50’35.6″ E, 22 November 2020, Felix Wäckers (received via Dominiek Vangansbeke), PBK 22-0905-035#slide1. Six paratype females, three paratype HDNs—FRANCE: Grand Est, Verzenay, Marcus Duarte, 8 April 2023, DV_2023-037.Depository. Holotype, paratypes —University of Michigan, Museum of Zoology, Ann Arbor, Michigan, USA. Paratypes (France)—Royal Belgian Institute of Natural Sciences, Brussels, Belgium.Etymology. The new species is named after the Belgian entomologist Peter Berx.Habitat. Thyreophagus berxi lives under the bark of small fallen branches of deciduous trees, such as European beech and birch trees.DescriptionFemale (n = 2) , 230  wide, 2.9 -times longer than wide. Idiosomal cuticle smooth. Subcapitular setae (h) long, widened basally; palp tibial setae (a), lateral dorsal palp tibial setae (sup), dorsal palp tarsal seta (cm) filiform; supracoxal seta elcp present, widened basally; terminal palp tarsal solenidion ω short, bacilliform; external part of terminal eupathidium ul’’ dome-shaped; terminal eupathidium ul’ small, dome-shaped. Prodorsal sclerite 98 (100) long, 94 (96) wide, 1.1 -times longer than wide, with setae vi , rounded anterolateral incisions, and elongate midlateral incisions (insertion points of setae ve). Prodorsal sclerite has three types of patterns: smoothly punctated , longitudinal lines , smoothly punctated smaller lines . Grandjean’s organ (GO) with 9–10 membranous finger-like extensions. Supracoxal seta (scx) smooth, sword-shaped, widened and flattened, tapering at tip, slightly curved. Idiosomal setae  smooth, filiform, medium length and slender; opisthosomal gland openings slightly anteriad of setal bases e2. Only one pair of fundamental cupules (ih) observed.Female . Idiosom1a, 3a, 4a, and 4b) and one pair of genital setae (g). Shape of coxal sclerites as in Ventral surface of idiosoma with four pairs of coxal setae  represented by small triangular rudiments; setae wa absent. Tarsus III with 10 setae; f, d, r filiform; e, w, s, u, v, p, q spiniform. Tarsus IV similar to tarsus III, except w filiform. Solenidion ω1 on tarsus I cylindrical, with clavate apex, bent and pointed outward, to posterior side of tarsus; solenidion ω1 on tarsus II simple, cylindrical, with clavate apex, not bent, shorter than ω1 on tarsus I. Solenidion ω2 on tarsus I shorter than ω1, cylindrical, with rounded apex, slightly widened at tip, situated slightly anterior and external to ω1. Solenidion ω3 on tarsus I cylindrical, with rounded apex, as long as ω1, longer than ω2. Famulus (ε) of tarsus I wide, spiniform, with broadly rounded apex. Solenidia φ of tibiae I–III elongate, tapering, well extending beyond apices of respective tarsi with ambulacra; solenidion φ IV shorter, shorter than tarsus IV (with ambulacra). On genu I, solenidion σ’ elongate, with rounded tip, reaching bases of φ I; σ’’ I distinctly wider than σ’, slightly not reaching bases of φ I. On genu II, solenidion σ short (more than three-times longer than its width), with rounded tip. Solenidion σ of genu III and IV absent.Legs short, all segments free. Trochanters I–III each with filiform seta, Male. Absent.Heteromorphic deutonymph (n = 1) (sup); setae h absent from subcapitular remnant, their positions marked by somewhat refractile spots. (n = 1) . Body elvi) apical, long, bases separated. A pair of lateral ocelli present on propodosoma; ocelli widely separated from each other (distance 50); lenses and pigmented spots present, maximum diameter of lenses 23. External vertical setae (ve) absent; external scapular setae se situated just below eye lenses; internal scapular setae (si) distinctly posterior and medial to external scapulars (se). Supracoxal setae of legs I (scx) filiform, situated below setae se. Sejugal furrow well-developed. Propodosomal sclerite 80, hysterosomal shield 180, ratio hysterosomal shield/propodosomal sclerite length = 2.25. Hysterosomal shield with 11 pairs of simple, filiform setae , setae h3 distinctly longer than others. Opisthonotal gland openings (gla) ventral; situated ventrally on hysterosomal shield, slightly posterior to setae c3. Of four fundamental pairs of cupules, only three pairs observed: ia posteriomedial of setae c2, im posterior to level of d2 and ih ventral, lateral to posterior sides of attachment organ.Dorsum. Propodosomal sclerite and hysterosomal shield smoothly punctate; distinct linear pattern present on anterior and lateral sides of propodosomal sclerite. A small area of linear pattern present on hysterosomal shield. Anterior end p of propodosoma shaped as obtuse triangle. Internal vertical setae (c3) long, filiform, situated ventrally between legs II–III, adjacent to region separating sternal and ventral shields. Coxal setae 1a, 3a reduced, represented by minute structures each situated in an alveolus. Setae 4b, g filiform; 4a small, rounded conoids, 4b longer than g. Genital region in posterior portion of coxal fields IV; genital opening elongate; there are two pairs of genital papillae; genital papillae two-segmented, with rounded apices. Coxal setae (4b) situated at anterior tips of coxal apodemes IV; genital setae (g) laterad of genital opening. Attachment organ posterior to coxal fields IV. Anterior suckers (ad3) round, median suckers (ad1+2) distinctly larger, with paired vestigial alveoli (not situated on a common sclerite); pair of small refractile spots anterolateral to median suckers (ps3); lateral conoidal setae of attachment organ (2ps) situated slightly posterior to line joining centers of median suckers, distinctly anterior conoidal setae (ps1) and slightly posterior to median suckers (ad1+2); anterior and posterior lateral and posterior median cuticular conoids well-developed; anus situated between anterior suckers (ad3).Venter. Coxal fields sclerotized, smoothly punctate. Anterior apodemes of coxal fields I fused forming sternum. Sternum not reaching posterior border of sternal shield by distance exceeding its length. Posterior border of sternal shield weakly sclerotized. Anterior apodemes of coxal fields II curved medially. Posterior apodemes of coxal fields II weakly developed, thin, sternal and ventral shield adjacent. Anterior apodemes of coxal fields III free. Posterior medial apodeme in area of coxal fields IV weakly expressed. Posterior apodemes IV absent. Subhumeral setae ; gT II shorter, filiform; setae kT III somewhat spiniform, kT IV and has a distinct prong. Tarsal setation 7-8-8-8. All pretarsi consisting of hooked empodial claws arising from tarsal apices, and short, paired condylophores within tarsal apices. Tarsus I with three filiform setae , three slightly foliate , and one spoon-shaped seta e; seta d elongated, longer than tarsus (its base situated at level of bases ra and la); seta s alveolar; setae wa, aa, and ba I absent; tarsus II similar to tarsus I except seta ba present and filiform, base of seta d posterior of bases ra and la. Tarsus III with eight setae  smooth; all setae, except d III foliate. Tarsus IV similar to tarsus III, except seta w filiform, with a distinct prong. Solenidia ω1 on tarsi I–II cylindrical, with slightly clavate apices, ω1 II longer than ω1 I. Solenidion ω3 on tarsus I longer and thinner than ω1, with rounded apex, positioned slightly anterior to ω1; ω1 and ω3 separated by bulbous famulus (ε). Solenidion ω2 of tarsus I thin, slightly widened apically, situated somewhat more basal and posterior to ω1+ε+ ω3 group. Solenidia φ of tibiae I–III elongate, tapering; φ I and III longer than tarsus I and III, respectively; φ II shorter than tarsus II; φ IV short. Solenidia σ of genu I elongate, slightly tapering, nearly reaching tip of tibia I; σ of genu II shorter, cylindrical, not reaching midlength of tibia II; σ of genu III absent.Legs. Legs elongate, all segments free. Trochanters I–III each with long, filiform seta, DiagnosisThyreophagus berxi is close to Th. spinitarsis  and Th. potawatomorum sp. n. by tarsi III with seven spiniform setae  and the prodorsal sclerite with linear striation extending over at least 75% of its length. Th. berxi differs from Th. spinitarsis by the vase-shaped atrium of the spermatheca, with the width in the central part two-times shorter than the width at the entrance to spermatheca . See above for the differences from Th. potawatomorum.Female. Th. berxi is close to Th. corticalis and Th. potawatomorum by the following characters: body elongate (more than 1.7-times longer than wide), setae hT and gT I–II present, different in shape, bases of seta d are at the level of bases of ra and la on tarsus I. Th. berxi differs from Th. corticalis by the following character states: the posterior medial apodeme is weakly developed ; the diameter of ocelli is about 23 ; setae wa I are absent ; seta kT IV with a distinct prong . See above for the differences from Th. potawatomorum.Heteromorphic deutonymph. FemalesTh. africanus , Th. javensis , Th. sminthurus , Th. johnstoni , Th. leclercqi , Th. rwandanus .Adults of the following species are unknown: species inquirendae): Th. aleurophagus , Th. angustus , Th. berlesianus , Th. entomophagus nominalis , Th. lignieri , Th. magnus , Th. polezhaevi , Th. ponticus .Not included .1 Very large species, body length > 1500 μm. Egypt………………………………………………………………………………- Smaller species, body length < 700 μm………………………………………………………………………………………………………………………………………2u and v on tarsi III–IV vestigial; seta wF IV absent. USA (Florida) …………………………………………………………………………………Th. hobe sp. n.2 Setae u and v on tarsi III–IV well-developed, spiniform; seta wF IV present……….……………………………………………………………………………………3.- Setae s, u and v) well-developed, proral setae p and q vestigial or absent…………………………………………4.3 Tarsus III with three ventral apical spiniform setae ……………………………………………………………………………………7.- Tarsus III with five ventral apical spiniform setae well-developed .4 Prodorsal sclerite wider than long, almost entirely punctate, with a few short longitudinal striations in posteromedian region; atrium of spermatheca in form of an inverted bell, with base 18–20 μm wide; seta w III small spine or absent…………………………………………………………………………………………………………………………………………………………………………………5- Prodorsal shield distinctly longer than wide, almost entirely covered with fine longitudinal striations; atrium of spermatheca smaller, not in form of a bell; seta Th. italicus .5 Prodorsal sclerite with linear striation in posterior half of shield. Italy……………………………………………………………………- Prodorsal sclerite with linear striation extending over at least 75% of its length………………………………………………………………………………………6w III a very short spine; seta se not longer than prodorsal shield. Morocco………………………………………………………………………………………………………Th. cooremani .6 Idiosomal length 270–360 μm, width 87–150 μm; atrium of spermatheca dome-shaped, wider (6 μm) than long (5 μm) and not narrowed toward its center; seta w III vestigial; seta se longer than prodorsal sclerite. Europe…………………………..Th. odyneri .- Idiosomal length 525–675 μm, width 210–280 μm; atrium of spermatheca vase-shaped, 12 μm long, maximum width 12 μm, narrowed toward the center where it 5 μm wide; narrowed toward middle and widened in its proximal part; seta w III filiform…………………………………………………………………………………………………………………………………………………………………87 Seta w III spiniform or vestigial…………………………………………………………………………………………………………………………………………………13- Seta 8 Anterior margin of prodorsal sclerite without paired indentations…………………………………………………………………………………………………………9- Anterior margin of prodorsal sclerite with paired indentations……………………………………………………………………………………………………………10Th. passerinus .9 Atrium of spermatheca weakly developed; sclerotized portion of spermatheca in form of a broad arc, much wider than long. Cuba …Th. plocepasseri .- Atrium of spermatheca well-developed, vase-shaped. Kenya…………………………………………………wa I absent. Ukraine…………………………………………………………………………………………………………Th. annae .10 Seta wa I present, spiniform or vestigial………………………………………………………………………………………………………………………………………11- Seta 11 Solenidion σ’ I longer than σ’’ I; prodorsal sclerite at most 1.3-times as long as wide...................................................................................................................12Th. evansi .- Solenidion σ’ I shorter than σ’’ I; prodorsal sclerite 1.5-times longer than wide. Ireland……………………………………………………………h2 and h3 with bases inflated, conical; base of spermatheca forming thin sclerotized arc that divided anteriorly into four short, fine sclerotized lines; genu I with solenidion σ’ short, 8 μm long, σ” 6 μm long (ratio 1.4:1); Great Britain ……………………………………………………………………………Th. macfarlanei .12 Long terminal setae h2 and h3 with very thin bases; atrium U-shaped with thick sides, 6 μm long, 5 μm wide; genu I with solenidion σ’ thin, 18–20 μm, σ” slightly thickened, 12 μm long (ratio 1.58: 1); Morocco …………………………………………………………………………………………………………………………………Th. athiasae .- Long terminal setae w III well-developed, spiniform…………………………………………………………………………………………………………………………………………1413 Seta w III vestigial………………………………………………………………………………………………………………………………………………………………25- Seta Th. ais). Base of spermatheca in form of a broad arc, much wider than long, or small and rounded …………………………………………………………………………………………………………………………………………1514 Solenidion σ II very short, 2–3-times longer than its width; atrium absent or minute, much shorter than sclerites of oviducts .16 Solenidion σ II short and filiform or nearly conical, but with sides straight and not convex; linear sclerites near the typical sclerites of oviducts present; paired sclerites of oviducts Y-shaped, not elongated, at least three-times longer than its width. Widespread ………………………………………………………...Th. vermicularis .- Solenidion σ II short and filiform; linear sclerites near the typical sclerites of oviducts absent; paired sclerites of oviducts elongated, more than five-times longer than their width, V-shaped. Great Britain ……………………………………………………………………………………………………………………………………vi nearly touching, situated in common unsclerotized area. USA (Florida)…………………………………………………………………………………Th. Calusorum .17 Paired sclerites of oviducts V-shaped; canal of spermatheca at entrance to spermatheca widened; bases of setae vi, separated, not in common area …………………………………………………………………………………………………………………………………………………………………………………………18- Paired sclerites of oviducts Y-shaped; canal of spermatheca at entrance to spermatheca, uniform in width, not widened; bases of setae 1 II five-times longer than its width; solenidion φ IV reaching middle of tarsus IV. Mauritius ………………………………………………………………………………………………………………………………Th. mauritianus .18 Cuplike portions of sclerites of oviducts distinctly shorter than their stems; solenidia σ’ and σ’’ subequal; solenidion ω1 II three-times longer than its width; solenidion φ IV longer, nearly reaching bases of setae d IV. USA (Florida) ……………………………………………………………………………………………………………………………………………Th. ais sp. n.- Cuplike portions of sclerites of oviducts subequal; solenidia σ’ distinctly longer than σ’’; solenidion ωwa I present…………………………………………………………………………………………………………………………………………………………………2019 Seta wa I absent…………………………………………………………………………………………………………………………………………………………………………21- Seta h1 less than half of length of h2. Colombia………………………………………………………………………………………………………………………………………Th. incanus .20 Anterior margin of prodorsal shield without paired indentations; prodorsal shield smoothly punctated; posterior hysterosomal seta h1 half of length of h2. Europe……………………………………………………………………………………………………………………………………………………Th. spinitarsis .- Anterior margin of prodorsal shield with paired indentations; prodorsal shield with linear striation extending over at least 75% of its length; posterior hysterosomal seta 21 With one pair of large, sclerotized, funnel-like, internal structures near posterior end of body (not to be confused with sclerites oviducts) ………………………22- Without paired, funnel-like structures in posterior body……………………………………………………………………………………………………………………………23Th. tridens .22 Solenidion φ of tibia IV very short (4 μm); USA  …………………………………………………………………………Th. cracentiseta Barbosa, .- Solenidion φ of tibia IV longer (14 μm). Brazil…………………………………………………………………………h1, h2, and h3 very long , similar in length. New Zealand……………………………Th. australis .23 Setae h2 and h3 less than 2.5-times longer than length of prodorsal shield, seta h1 less than half of length of h2………………………………………………………………24- Setae vi short, not extending beyond anterior margin of prodorsum; bases of vi touching; medial area of prodorsal shield with non-uniform pattern of striations in its anterior and posterior parts; setae h2 and h3 shorter than anus; rounded sclerotized capsule at junction of canal of spermatheca and atrium present. USA (Michigan)………………………………………………………………………………………………………………………………………………………Th. potawatomorum sp. n.24 Setae vi long, extending beyond anterior margin of prodorsum; bases of setae vi distinctly separated; entire medial area of prodorsal shield uniformly striated; setae h2 and h3 longer than anus; rounded capsule at junction of canal of spermatheca and atrium absent. France, Belgium, Germany……………………………………………………………Th. berxi sp. n.- Setae h2 and h3 1.1–1.25-times longer than length of prodorsal shield; diameter of genital papillae approximately six-times shorter than length of genital setae. Palaearctic ………………………………………………………………………………………………………………………………………………………………………Th. corticalis .25 Setae h2 and h3, long, their lengths 1.75-times longer than length of prodorsal shield; diameter of genital papillae approximately four-times shorter than length of genital setae. USA (Michigan), Canada (Ontario) …………………………………………………………………………………………………………………………………………Th. ojibwe sp. n.- Setae Males (modified after )Th. africanus , Th. javensis , Th. sminthurus , Th. johnstoni , Th. leclercqi , and Th. rwandanus .Adults of the following species are unknown: species inquirendae): Th. aleurophagus , Th. angustus , Th. berlesianus , Th. entomophagus nominalis , Th. lignieri , Th. magnus , Th. polezhaevi , and Th. ponticus .Not included : Th. aleurophagus, Th. angustus, Th. berlesianus, Th. italicus, Th. lignieri, Th. magnus, and Th. ponticus.Not included .2 Posterior venter with sclerotized projection very poorly developed or absent. Colombia…………………………………………………….- Posterior venter with sclerotized projection well-developed…………………………………………………………………………………………………………………………3Th. cynododactylon .3 Body elongate, six-times longer than wide; large species, length > 700 μm. Egypt……………………………………………….- Body ovoid, 1.5–2-times longer than wide; small species, length < 500 μm. Widespread……………………………………………………………………………………………...4s, u, v, p, q), three filiform setae , and two suckers . Ireland…………………………………………………….Th. evansi .4 Tarsus IV with five spine-like setae , three filiform setae , and two suckers . Widespread………………Th. entomophagus .- Tarsus IV with three spine-like setae .6 Entire width of prodorsal sclerite covered by longitudinal striation. Europe……………………………………………………………………………- Longitudinal striation on prodorsal sclerite restricted to median region, lateral areas simply punctulate……………………………………………………………………………7h2 and h3 1.1–1.25-times longer than length of prodorsal shield; spines p, q, and u, v III–IV subequal. Palaearctic…………………………..Th. corticalis .7 Setae h2 and h3 long, their lengths are 1.8-times longer than the length of the prodorsal shield; spines p and q shorter than spines u and v on tarsi III–IV. USA (Michigan), Canada (Ontario). …………………………………………………………………………………………………………………………………………………………………………………Th. ojibwe sp. n.- Setae e2. Ukraine……………………………..Th. annae .8 Posterior hysterosoma with a large sclerotized area extending posteriad from level of setae h1…………………………………………………………………………9- Posterior hysterosoma unsclerotized or at most with short terminal sclerotization posterior to setae h1…………………………………………………………………………………………………………………109 Posterior idiosoma with short sclerotized area posterior to setae - Posterior idiosoma unsclerotized…………………………………………………………………………………………………………………………………………………………11Th. gallegoi .10 Genu I with solenidia σ’ and σ” approximately equal in length. Widespread……………………………………………………………Th. passerinus .- Genu I with solenidion σ’ only half of length of σ”. Cuba………………………………………………………………………………………………d2 and e2 much longer than distance between their alveoli. New Zealand………………………Th. australis .11 Dorsal hysterosomal setae relatively long, setae d2 and e2 shorter than distance between their alveoli. Brazil……….Th. cracentiseta .- Dorsal hysterosomal setae much shorter, setae Heteromorphic deutonymphsTh. aleurophagus, Th. angustus, Th. annae, Th. athiasae, Th. cooremani, Th. cracentiseta, Th. cynododactylon, Th. entomophagus nominalis, Th. evansi, Th. gallegoi, Th. hobe, Th. incanus, Th. italicus, Th. macfarlanei, Th. magnus, Th. mauritianus, Th. ojibwe, Th. odyneri, Th. passerinus, Th. plocepasseri, Th. polezhaevi, Th. ponticus, Th. spinitarsis, Th. tridens, and Th. vermicularis.Unknown for the following species: species inquirendae): Th. berlesianus, Th. lignieri.Not included  were corrected.Published measurements of Th. africanus .1 Dorsal surface completely striated. Afrotropical………………………………………………………………………………………………………………- Dorsal surface smoothly punctate, without striations…………………………………………………………………………………………………………………………………………22 Body ovoid, 1.3–1.5-times longer than wide…………………………………………………………………………………………………………………………………………………3- Body elongate, more than 1.7-times longer than wide…………………………………………………………………………………………………………………………………………5hT I more than half the length of gT I. Europe………………………………………………………………………………………………………………….Th. leclercqi .3 Seta hT I less than half the length of gT I……………………………………………………………………………………………………………………………………………………4- Seta c3 and cp; seta kT III filiform; setae wa I–II absent. Widespread…Th. entomophagus .4 Opisthonotal gland openings approximately equidistant from setae c3 than to dorsolateral seta cp; seta kT III with distinct prong; setae wa I-II present. New Zealand…Th. australis .- Opisthonotal gland openings much closer to ventral seta 5 Hysterosomal sclerite about 1.7-times longer than prodorsal sclerite…………………………………………………………………………………………………………………6- Hysterosomal sclerite about two-times longer than prodorsal sclerite…………………………………………………………………………………………………………………7hT I absent; posterior medial apodeme in area of coxal fields IV present; seta kT III with distinct prong. Great Britain, USA (Washington) …Th. sminthurus .6 Seta hT I present; posterior medial apodeme in area of coxal fields IV absent; seta kT III without prong, filiform. USA (Maryland)………………………Th. johnstoni .- Seta hT II and gT II subequal ………………………………………………………………………………………………………………………………………………………………………87 Setae hT II twice the length of gT II…………………………………………………………………………………………………………………………………………………………………9- Setae hT II and gT II filiform, both subequal to tibia II. Java………………………………………………………………………………………………Th. javensis .8 Setae hT II and gT II spiniform, shorter than half the length of tibia. Afrotropical………………………………………………………………………………Th. rwandanus .- Setae d situated at the same level with bases of setae ra and la; diameter of ocellus 16–23 μm …………………………………………………………………109 On tarsus I, bases of setae d distal to bases of setae ra and la; diameter of ocellus 10–14 μm …………………………………………………………………………………………….12- On tarsus I, bases of setae Th. potawatomorum sp. n.10 Width of ocellus 16 μm, distance between ocelli 36 μm; posterior medial apodeme in area of coxal fields IV present. USA (Michigan)………………..- Width of ocellus about 18–23 μm, distance between ocelli about 40–50 μm; posterior medial apodeme in area of coxal fields IV weakly developed or absent………………….11kT IV with distinct prong; width of ocellus 23 μm, distance between ocelli 50 μm; posterior medial apodeme in area of coxal fields IV weakly developed. Europe……………………………………………………………………………………………………………………………………………………………………………………Th. berxi sp. n.11 On tibia IV, seta kT IV without prong; width of ocellus about 18–19 μm, distance between ocelli about 40–42 μm; posterior medial apodeme in area of coxal fields IV absent. Widespread………………………………………………………………………………………………………………………………………………………………Th. corticalis .- On tibia IV, seta p and q on tarsus IV foliate; seta d III shorter than leg III; setae d IV shorter or slightly longer than leg IV; diameter of ocellus 10–13. USA (Florida)……………………………………………………………………………………………………………………Th. calusorum 12 Tarsal setae p and q on tarsus IV short, spiniform; setae d III longer than leg III, d IV distinctly longer than leg IV; diameter of ocellus 12–14. USA (Florida)……….Th. ais sp. n.- Tarsal setae


In this paper, the authors introduce the anisotropic Hardy space of Musielak-Orlicz type, HAφ(ℝn), via the grand maximal function. The authors then obtain some real-variable characterizations of HAφ(ℝn) in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space HAp(ℝn) with p ∈ , and, as an application, the authors prove that, for a given admissible triplet , if T is a sublinear operator and maps all -atoms with q < ∞ -atoms with q = ∞) into uniformly bounded elements of some quasi-Banach spaces ℬ, then T uniquely extends to a bounded sublinear operator from HAφ(ℝn) to ℬ. These results are new even for anisotropic Orlicz-Hardy spaces on ℝn. Let  Moreover, there were several efforts to extend classical Hardy spaces, some of which are weighted anisotropic Hardy spaces  denote the class of Muckenhoupt weights →)., Bownik  showed tt al. in , page 19t al. in , via usiand Zhou  proved ta et al.  establispaces in , weightepaces in , and, espaces in .HAφ(ℝn), via grand maximal functions and characterize these spaces via anisotropic atomic decompositions. These Hardy spaces include classical Hardy spaces Hp(ℝn) of Fefferman and Stein  for all x, y ∈ ℝn, where H ∈ 2/i(φ), ∞). Then there exists a positive constant C such that, for all K ∈ ℤ, L ∈ 2/i(φ), ∞). If k ≤ K and x − y ∈ Bk, thenF0K∗, is as in ]2/i(φ), ∞), we choose p < i(φ) large enough and q > q(φ) small enough such that Np − q2 > 0. Therefore, from this, f implies . This fiThe following Lemmas ψ ∈ 𝒮(ℝn) with ∫nℝψ(x)dx ≠ 0. Then, for any given N, L ∈ 2/i(φ), ∞), we know that there exists a positive integer m such that, for all f ∈ 𝒮′(ℝn), x ∈ ℝn, and integers K ∈ ℤ+,f ∈ 𝒮′(ℝn) and K ∈ ℤ+,K → ∞, by the monotone convergence theorem and the continuity of φ  ⇒ ⇒25) ⇒ . Let φ b ≠ 0. By  of Lemma, ·) see , we haveℳψ0f ∈ Lφ(ℝn). By L ∈  such that (f ∈ Lφ(ℝn) for all K ∈ ℤ+. By Lemmas m ∈ ℕ such thatC1 being independent of K ∈ ℤ+. For any given K ∈ ℤ+, letC2≔[2C1]p1/ with p ∈ ). We claim thatp of φ and C2p−C1 = 1/2, we havex ∈ ΩK and p ∈ ), we choose q ∈  small enough such that 1/q > q(φ), where q(φ) is as in  such that, for all integers K ∈ ℤ+ and x ∈ ΩK,φ is of uniformly upper type 1 and positive lower type p with p < i(φ), it follows that q and lower type p/q. Consequently, using  but is independent of K ∈ ℤ+. This inequality is crucial, since it gives a bound of the nontangential maximal function by the radial maximal function in Lφ(ℝn).Suppose uch that  holds truch that∫ℝnφf(f(x) converges pointwise and monotonically to ℳψf(x) for all x ∈ ℝn as K → ∞, it follows that ℳψf ∈ Lφ(ℝn) by  , and the monotone convergence theorem, we conclude that ||ℳψf||Lφ(ℝn) ≤ C4||ℳψ0f||Lφ(ℝn), where now the positive constant C4 corresponds to L = 0 and is independent of f ∈ 𝒮′(ℝn). Combining this, (Since φ(ℝn) by , the con, ·) see , and thend using , the conng this, , and Lemn established in . We denote by Lφq(ℝn) the usually anisotropic weighted Lebesgue space with the anisotropic Muckenhoupt weight φ. Then we have the following technical lemma (see  and f ∈ Lφq(ℝn), then the series ∑ibi converges in Lφq(ℝn), and there exists a positive constant C6, independent of f and λ, such that ||∑i|bi|||Lφq(ℝn) ≤ C6||f||Lφq(ℝn).If The following conclusion is essentially  and q ∈ (q(φ), ∞).(i)m ≥ s ≥ ⌊q(φ)lnb/(i(φ)lnλ−)⌋ and f ∈ Hm,Aφ(ℝn), then gm* ∈ Lφq(ℝn), and there exists a positive constant C8, independent of f and λ, such thatIf (ii)m ∈ ℕ and f ∈ Lφq(ℝn), then g ∈ L∞(ℝn), and there exists a positive constant C9, independent of f and λ, such that ||g||L∞(ℝn) ≤ C9λ.If Let f ∈ Hm,Aφ(ℝn), by ibi converges in Hm,Aφ(ℝn) and therefore in 𝒮′(ℝn) by ti(x) is as in m ≥ ⌊q(φ)lnb/(i(φ)lnλ−)⌋ implies that (λ−)m+1 > bq(φ). Moreover, for any fixed x ∈ xi + (Bt+ℓi+2σ+1∖Bt+ℓi+2σ) with t ∈ ℤ+, we find thatLφqq(φ)(ℓq(φ))-boundedness of the vector-valued maximal function ℳA ), we find thatfm* ≤ λ on Ω∁, for any x ∈ Ω∁, usingNoticing that tes with , we obtaf ∈ Lφq(ℝn), then g and {bi}i are functions. By ibi converges in Lφq(ℝn) and hence in 𝒮′(ℝn) due to the fact that Lφq(ℝn) ⊂ 𝒮′(ℝn) is continuous embedding (see ⌋ ≤ s ≤ m and height λ associated with fm* as in g and bi in gλ and biλ, respectively. By  as λ → ∞. Moreover, by gm*)λ ∈ Lφq(ℝn), which, together with gλ ∈ Lφq(ℝn). This finishes the proof of Let vely. By  of LemmaHAφ(ℝn) and anisotropic atomic Hardy spaces of Musielak-Orlicz type HAφ,q,s(ℝn)  see  below.ℬ≔{B = x + Bk : x ∈ ℝn, k ∈ ℤ} be the collection of all dilated balls.Let B ∈ ℬ and q ∈ , let Lφq(B) be the set of all measurable functions f, supported in B, such thatFor any Lφq(B), ||·||Lφq(B)) is a Banach space. Next we introduce anisotropic atomic Hardy spaces of Musielak-Orlicz type.It is easy to show that ((i)φ, q, s) is said to be admissible, if q ∈ (q(φ), ∞] and s ∈ ℤ+ such that s ≥ m(φ) with m(φ) as in (An anisotropic triplet (φ) as in .(ii)φ, q, s), a measurable function a is called an anisotropic  -atom ifFor an admissible anisotropic triplet ((a)a ∈ Lφq(B) for some B ∈ ℬ;(b)a||Lφq(B) ≤ ||χB||Lφ(ℝn)−1;||(c)nℝa(x)xαdx = 0 for any |α | ≤s.∫(iii)φ, q, s), the anisotropic atomic Hardy space of Musielak-Orlicz type, HAφ,q,s(ℝn), is defined to be the set of all distributions f ∈ 𝒮′(ℝn) which can be represented as a sum of multiples of anisotropic -atoms, that is, f = ∑jaj in 𝒮′(ℝn), where aj for j is a multiple of an anisotropic -atom supported in the dilated ball xj + Bℓj, with the propertyFor an admissible anisotropic triplet , where {aj}j are -atoms supported in dilated balls {xj + Bℓj}j, andf as above withHAφ,q,s(ℝn) coincide with equivalent (quasi)norms.(i) In f = ∑jλjaj in 𝒮′(ℝn) for some -atoms, {aj}j, and {λj}j ⊂ ℂ such that Indeed, if 𝒮′(ℝn) with f = ∑jλjaj and Conversely, if φ is as in (A∞(ℝn) Muckenhoupt weight w and Φ(t)≔tp for all t ∈ ⌋, and let f ∈ Hm,Aφ(ℝn). For each k ∈ ℤ, as in f has a Calderón-Zygmund decomposition of degree s and height λ = 2k associated with fm* as follows:k ∈ ℤ, {xik}i≔{xi}i is a sequence in Ωk and {ℓik}i≔{ℓi}i is a sequence of integers such that  with respect to the norms given by ζik onto 𝒫s(ℝn) with respect to the norm associated with ζjk+1 given by (𝒫s(ℝn) such that, for all Q ∈ 𝒫s(ℝn),To obtain the conclusion uch that  through uch that  hold forgiven by , and {Pgiven by . Moreovegiven by , namely,Lemmas ℓjk+1 ≤ ℓik + σ and If i, L is as in ∩(Ωk+1)∁.There exists a positive constant k ∈ ℤ, ∑i∑jPi,jk+1ζjk+1 = 0, where the series converges pointwise and also in 𝒮′(ℝn).For every The proof of the following lemma is similar to that of ⌋ and let q ∈ (q(φ), ∞). Then, for any f ∈ Lφq(ℝn)∩Hm,Aφ(ℝn), there exists a sequence {aik}k∈ℤ,i of multiples of -atoms such that f = ∑k∈ℤ∑iaik converges almost everywhere and also in 𝒮′(ℝn), andC, independent of f, such that, for all k ∈ ℤ and i,λ ∈ ,Let f ∈ Hm,Aφ(ℝn)∩Lφq(ℝn). For each k ∈ ℤ, f has a Calderón-Zygmund decomposition of degree s ≥ ⌊q(φ)lnb/[i(φ)ln(λ−)]⌋ and height 2k associated with fm*, f = gk + ∑ibik as above. The conclusions  and 𝒮′(ℝn) as k → ∞. It follows, from gk||L∞(ℝn) → 0 as k → −∞, which further implies that gk → 0 almost everywhere as k → −∞, and, moreover, by the fact that L∞(ℝn) is continuously embedding into 𝒮′(ℝn) (see ⌋ and q ∈ (q(φ), ∞], then HAφ,q,s(ℝn) = Hm,Aφ(ℝn) = HAφ(ℝn) with equivalent (quasi)norms.Let be as in . If m ≥ m ≥ s ≥ ⌊q(φ)lnb/[i(φ)lnλ]⌋, and all the inclusions are continuous. Thus, to finish the proof of f ∈ Hm,Aφ(ℝn) with m ≥ s ≥ ⌊q(φ)lnb/[i(φ)lnλ]⌋, ||f||HAφ,∞,s(ℝn)≲||f||Hm,Aφ(ℝn), which implies that Hm,Aφ(ℝn) ⊂ HAφ,∞,s(ℝn).Observe that, by , Definitf ∈ Hm,Aφ(ℝn)∩Lφq(ℝn); by To this end, let f ∈ Hm,Aφ(ℝn). By fk}k∈ℕ of functions in Hm,Aφ(ℝn)∩Lφq(ℝn) such that ||fk||Hm,Aφ(ℝn) ≤ 2k−||f||Hm,Aφ(ℝn) and f = ∑k∈ℕfk in Hm,Aφ(ℝn). By k ∈ ℕ, fk has an atomic decomposition fk = ∑i∈ℕdik in 𝒮′(ℝn), where {dik}i∈ℕ are multiples of -atoms with suppdik ⊂ xik + Bℓik. Sincef = ∑k∈ℕ∑i∈ℕdik ∈ HAφ,∞,s(ℝn) andLet HAφ(ℝn) the anisotropic Hardy space Hm,Aφ(ℝn) of Musielak-Orlicz type with m ≥ m(φ).For simplicity, from now on, we denote simply by HAφ(ℝn), and, as an application, a bounded criterion on HAφ(ℝn) of quasi-Banach space-valued sublinear operators is also obtained.The goal of this section is to obtain the finite atomic decomposition characterization of q < ∞ (or continuous atoms when q = ∞), its norm in HAφ(ℝn) can be achieved via all its finite atomic decompositions. This extends the conclusion p for all x ∈ ℝn and t ∈  with p ∈  and φ as in  as in  an admissible triplet.q ∈ (q(φ), ∞), then ||·||HA,finφ,q,s(ℝn) and ||·||HAφ(ℝn) are equivalent quasinorms on HA,finφ,q,s(ℝn).If HA,finφ,∞,s(ℝn) and ||·||HAφ(ℝn) are equivalent quasinorms on HA,finφ,∞,s(ℝn)∩ℂ(ℝn).||·||Let φ) as in , and  ⊂ HAφ(ℝn) and, for all f ∈ HA,finφ,q,s(ℝn),f ∈ HA,finφ,q,s(ℝn) when q ∈ (q(φ), ∞) and for all f ∈ HA,finφ,q,s(ℝn)∩ℂ(ℝn) when q = ∞, ||f||HA,finφ,q,s(ℝn)≲||f||HAφ(ℝn).Obviously, by Now we prove this by three steps.Step  1 ). Assume that q ∈ (q(φ), ∞]. Without loss of generality, we may assume that f ∈ HA,finφ,q,s(ℝn) and ||f||HAφ(ℝn) = 1. Notice that f has compact support. Suppose that suppf ⊂ B≔Bk0 for some k0 ∈ ℤ, where Bk0 is as in k ∈ ℤ, letq ∈ (q(φ), ∞) and q = ∞, by aik}k∈ℤ,i of multiples of -atoms such that f = ∑k∈ℤ∑iaik holds almost everywhere and in 𝒮′(ℝn). Moreover, by HAφ,∞,s(ℝn) ⊂ HAφ,q,s(ℝn) and m(φ), such that x ∈ (B*)∁≔(Bk0+4σ)∁. Hence, for all x ∈ (B*)∁, we haveOn the other hand, by Step  2 of the proof of  and q1 ∈ ), by Hölder's inequality and φ ∈ 𝔸q/q1(A), we havef ⊂ B and f has vanishing moments up to order s, we know that f is a multiple of a -atom and therefore f* ∈ L1(ℝn). Then, by  This, together with the vanishing moments of aik, implies that ℓ has vanishing moments up to order s and, hence, so does h by h = f − ℓ. Using χB||Lφ(ℝn)−1 ~ ||χB*||Lφ(ℝn)−1, we obtainC0, independent of f, such that h/C0 is a -atom, and, by φ, q, s)-atom for any admissible triplet . Then, by , 116), , Step  2Then, by , and ). Let q ∈ (q(φ), ∞). We first show ∑k>k′∑iλikaik ∈ Lφq(ℝn). For any x ∈ ℝn, since ℝn = ∪k∈ℤ(Ωk∖Ωk+1), there exists j ∈ ℤ such that x ∈ (Ωj∖Ωj+1). Since suppaik ⊂ Bℓik+σ ⊂ Ωk ⊂ Ωj+1 for k > j, applying x ∈ (Ωj∖Ωj+1),f ∈ Lφq(B) ⊂ Lφq(B*), we further have f* ∈ Lφq(B*). Since φ satisfies the uniformly locally dominated convergence condition, it follows that ∑k>k′∑iλikaik converges to ℓ in Lφq(B*).K, letℓK≔∑i,k)∈FK(λikaik. Since ∑k>k′∑iλikaik converges in Lφq(B*), for any ϵ ∈ , if K is large enough, we have that (ℓ − ℓK)/ϵ is a -atom. Thus, f = h + ℓK + (ℓ − ℓK) is a finite linear combination of atoms. By ; then aik is also continuous by examining its definition (see (f*(x) ≤ Cn,m(φ)||f||L∞(ℝn) for any x ∈ ℝn, where the positive constant Cn,m(φ) only depends on n and m(φ), it follows that the level set Ωk is empty for all k satisfying that 2k ≥ Cn,m(φ)||f||L∞(ℝn). We denote by k′′ the largest integer for which the above inequality does not hold. Then the index k in the sum defining ℓ will run only over k′ < k ≤ k′′.To prove (ii), assume that ion (see ). Since ϵ ∈ . Since f is uniformly continuous, it follows that there exists a δ ∈  such that if ρ(x − y) < δ, then |f(x) − f(y)|<ϵ. Write ℓ = ℓ1ϵ + ℓ2ϵ with ℓ1ϵ≔∑i,k)∈F1∈F2 : bℓik+σ < δ, k′ < k ≤ k′′}.Let k ∈ . Since ϵ is arbitrary, we can hence split ℓ into a continuous part and a part that is uniformly arbitrarily small. This fact implies that ℓ is continuous. Thus, h = f − ℓ is a multiple of a continuous -atom by Step  2.On the other hand, for any fixed integer k′′], by  of Lemmaf. Let us use again the splitting ℓ≔ℓ1ϵ + ℓ2ϵ. By -atoms andℓ, ℓ1ϵ are continuous and have vanishing moments up to order s and, hence, so does ℓ2ϵ = ℓ − ℓ1ϵ. Moreover, suppℓ2ϵ ⊂ B* and ||ℓ2ϵ||L∞(ℝn) ≤ C1(k′′ − k′)ϵ. Thus, we can choose ϵ small enough such that ℓ2ϵ becomes a sufficient small multiple of a continuous -atom; that is,f = h + ℓ1ϵ + ℓ2ϵ is a finite linear combination of continuous atoms. Then, by -atom, we haveNow we can give a finite atomic decomposition of 2ϵ. By , the partoms and||ℓ1ϵ||HAHAφ(ℝn) of quasi-Banach-valued sublinear operators.As an application of the finite atomic decompositions obtained in  quasi-Banach space  ℬ is a vector space endowed with a quasinorm ||·||ℬ which is nonnegative, nondegenerate , and homogeneous and obeys the quasitriangle inequality; that is, there exists a constant K ∈ ))ℓp, Lwγ-quasi-Banach space ℬγ with γ ∈ −T(g)||ℬγ ≤ ||T(f−g)||ℬγ.For any given T is linear, then T is ℬγ-sublinear. Moreover, if ℬγ≔Lwq(ℝn) with q ∈ , w is a Muckenhoupt A∞ weight, and T is sublinear in the classical sense, then T is also ℬγ-sublinear.We remark that, if φ, q, s) be an admissible triplet. Assume that φ is an anisotropic growth function satisfying the uniformly locally dominated convergence condition and being of uniformly upper type γ ∈ q ∈ (q(φ), ∞), and T : HA,finφ,q,s(ℝn) → ℬγ is a ℬγ-sublinear operator such that(ii)T is a ℬγ-sublinear operator defined on continuous -atoms such that T has a unique bounded ℬγ-sublinear operator extension HAφ(ℝn) to ℬγ.then Let , by λj}j=1k and -atoms {aj}j=1k supported in balls {xj + Bℓj}j=1k such that f = ∑j=1kλjaj pointwise. By φ is of uniformly upper type γ, it follows that there exists a positive constant Cγ such that, for all x ∈ ℝn, s ∈ [1, ∞), and t ∈ ,j0 ∈ {1,…, k} such that Cγ|λj0|γ ≥ ∑j=1k|λj|γ, thenHA,finφ,q,s(ℝn) is dense in HAφ(ℝn), a density argument then gives the desired conclusion.Suppose that the assumption (i) holds true. For any  ,φ≤Cf ∈ HA,finφ,∞,s(ℝn)∩ℂ(ℝn), ||T(f)||ℬγ≲||f||HAφ(ℝn). To extend T to the whole HAφ(ℝn), we only need to prove that HA,finφ,∞,s(ℝn)∩ℂ(ℝn) is dense in HAφ(ℝn). Since Hφ,finp,∞,s is dense in HAφ(ℝn), it suffices to prove HA,finφ,∞,s(ℝn)∩ℂ(ℝn) is dense in Hφ,finp,∞,s in the quasinorm ||·||HAφ(ℝn). Actually, we only need to show that HA,finφ,∞,s(ℝn)∩ℂ∞(ℝn) is dense in HA,finφ,∞,s(ℝn) due to Suppose now that the assumption (ii) holds true. Similar to the proof of (i), by f ∈ HA,finφ,∞,s(ℝn). Since f is a finite linear combination of functions with bounded supports, it follows that there exists l ∈ ℤ such that suppf ⊂ Bl. Take ψ ∈ 𝒮(ℝn) such that suppψ ⊂ B0 and ∫nℝψ(x)dx = 1. By (ψk∗f) ⊂ Bl+σ for any −k < l, and f∗ψk has vanishing moments up to order s, where ψk(x)≔bkψ(Akx) for all x ∈ ℝn. Hence, f∗ψk ∈ HA,finφ,∞,s(ℝn)∩ℂ∞(ℝn).To see this, let  = 1. By , it is ef − f∗ψk) ⊂ Bl+σ for any −k < l, and f − f∗ψk has vanishing moments up to order s. Take any q ∈ (q(φ), ∞). By [φ satisfies the uniformly locally dominated convergence condition, we know thatf − f∗ψk = ckak for some -atom ak, where ck is a constant depending on k and ck → 0 as k → ∞. Thus, we obtain ||f−f∗ψk||HAφ(ℝn) → 0 as k → ∞. This finishes the proof of Likewise, supp(


Laryngeal hypersensitivity may be an important component of the common disorders of laryngeal motor dysfunction including chronic refractory cough, pdoxical vocal fold movement , muscle tension dysphonia, and globus pharyngeus. Patients with these conditions frequently report sensory disturbances, and an emerging concept of the ‘irritable larynx’ suggests common features of a sensory neuropathic dysfunction as a part of these disorders. The aim of this study was to develop a Laryngeal Hypersensitivity Questionnaire for patients with laryngeal dysfunction syndromes in order to measure the laryngeal sensory disturbance occurring in these conditions.The 97 participants included 82 patients referred to speech pathology for behavioural management of laryngeal dysfunction and 15 healthy controls. The participants completed a 21 item self administered questionnaire regarding symptoms of abnormal laryngeal sensation. Factor analysis was conducted to examine correlations between items. Discriminant analysis and responsiveness to change were evaluated.The final questionnaire comprised 14 items across three domains: obstruction, pain/thermal, and irritation. The questionnaire demonstrated significant discriminant validity with a mean difference between the patients with laryngeal disorders and healthy controls of 5.5. The clinical groups with laryngeal hypersensitivity had similar abnormal scores. Furthermore the Newcastle Laryngeal Hypersensitivity Questionnaire (LHQ) showed improvement following behavioural speech pathology intervention with a mean reduction in LHQ score of 2.3.The Newcastle Laryngeal Hypersensitivity Questionnaire is a simple, non-invasive tool to measure laryngeal pesthesia in patients with laryngeal conditions such as chronic cough, pdoxical vocal fold movement , muscle tension dysphonia, and globus pharyngeus. It can successfully differentiate patients from healthy controls and measure change following intervention. It is a promising tool for use in clinical research and practice. Laryngeal Dysfunction Syndromes include chronic refractory cough, pdoxical vocal fold movement , muscle tension dysphonia and globus pharyngeus. These conditions present to clinicians as discrete syndromes based around a dominant manifestation of a disordered laryngeal adductor reflex, e.g. cough, vocal fold closure, vocalisation, or swallowing ,2. They Abnormal sensory experience is characterised in three ways: (1) hypersensory–sensation triggered by stimuli that is sub-threshold for triggering that sensation, (2) pesthesia–altered sensory experience, and (3) allodynia–sensation triggered by stimuli that do not normally trigger those sensations. This characterisation can be applied to the concept of abnormal laryngeal sensation ,8.Patients with laryngeal dysfunction syndromes such as chronic refractory cough, pdoxical vocal fold movement, globus pharyngeus and muscle tension dysphonia frequently report irritation and discomfort in the laryngeal region. The focus of treatment in these conditions involves motor rather than sensory areas of dysfunction. There are standardised tests to measure sensory laryngeal dysfunction such as cough reflex sensitivity testing, Fibreoptic Endoscopic Evaluation with Sensory Testing (FEEST) and hypertonic saline challenge. While these tests provide objective reliable data they are expensive to administer and are rarely available outside of specialist treatment areas. Furthermore, these tests do not quantify the patient experience of the discomfort. Several questionnaires exist to measure quality of life in patients with voice disorders  and chroIn this study, we have developed and tested a questionnaire to document the laryngeal sensory abnormalities reported in these syndromes. The aim of this study was to develop a Laryngeal Hypersensitivity Questionnaire for patients with laryngeal dysfunction syndromes and to measure the laryngeal sensation occurring in these conditions. This paper describes the development and validation of the Newcastle Laryngeal Hypersensitivity Questionnaire which is a self-rated measure of laryngeal sensation.A total of 97 participants were studied. For the item validation and discriminant analysis, we studied 53 participants comprising healthy controls (n = 15) and 4 clinical groups: chronic refractory cough (n = 11), pdoxical vocal fold movement , globus pharyngeus (n = 6), and muscle tension dysphonia(n = 3). The case groups were recruited from consecutive referrals to the speech pathology department for assessment and treatment of their laryngeal condition. Exclusion criteria for all groups included recent (past month) upper respiratory tract infection, current smoking, untreated asthma, rhinitis or gastroesophageal reflux, significant psychological factors or neurological impairment preventing participation.For the study of questionnaire responsiveness, the questionnaire was administered to an additional group of 44 participants with laryngeal dysfunction syndromes. These participants included chronic refractory cough (n = 38), PVFM (n = 4) and globus pharyngeus (n = 2).1. Chronic Refractory Cough. The participants with chronic refractory cough had been referred by respiratory physicians for behavioural management of cough . The cou2. pdoxical Vocal Fold Movement. The participants with pdoxical vocal fold movement were diagnosed by either respiratory physicians or otolaryngologists. These patients had been referred for behavioural management of their respiratory symptoms which included inspiratory dyspnoea, noisy breathing and throat tightness. Asthma and other pulmonary diseases had been discounted as a reason for the respiratory problems in this group. They had positive symptoms of PVFM and a fall in FIF50 of greater than 20%.3. Globus Pharyngeus. The third group with globuspharyngeus were referred for clinical assessment and management of swallowing. These participants presented with globus sensation such as a sensation of an irritation, lump or tightness in the throat in the absence of oropharyngeal dysphagia.4. Muscle Tension Dysphonia. The fourth group included patients with muscle tension dysphonia diagnosed by otolaryngologists referred for dysphonia. These patients had a deviation in perceptual voice quality along with excessive tension in the intrinsic and/or extrinsic laryngeal muscles  in the a5. Healthy Controls. The healthy controls were recruited from the Hunter Medical Research Institute Healthy Control Register (n = 10), from a previous study where they served as healthy controls (n = 2) and by word of mouth (n = 3). All healthy controls had no history of voice disorder, chronic cough or extrathoracic airway hyperrresponsiveness. Voice was judged as within normal limits by a qualified speech pathologist. Healthy controls were also excluded if there was presence of asthma, presence of post-nasal drip syndrome, presence of gastro-oesophageal reflux, symptoms of breathing, cough or voice difficulty and/or swallowing difficulty.Written consent was obtained for all participants. The study was approved by the Hunter New England Research Ethics Committee.Item generation: Potential questionnaire items were generated by reviewing literature regarding sensations in chronic pain and neuropathy and from previous patient reports of laryngeal discomfort . These r1 equates to all of the time and 7 equates to none of the time (Appendix I). A lower score denotes greater impairment with sensory symptoms. This scaling is similar to the Leicester Cough Questionnaire.Item scaling: The items were rated on a 7 point Likert scale where Participants completed the 21 item questionnaire prior to their initial assessment in speech pathology. Reproducibility was assessed in a subgroup.In order to document the changes following therapy a revised 14 item version of the questionnaire was administered to a further group of 44 participants with laryngeal dysfunction syndromes.Descriptive statistics were obtained for each item. Items with a low mean rating i.e. that indicates the symptom occurs more frequently, were compared to other symptoms to determine whether there was a correlation. A correlation matrix was conducted and rotation component matrix was performed. Factor analysis and item reduction were also completed. Discriminant validity was assessed by one way anova which was conducted on the final questionnaire to determine whether there was a significant difference (1) between the clinical groups, and (2) between the clinical groups and healthy controls. Questionnaire responsiveness was assessed by comparing pre-post treatment data using a Wilcoxon test. Significance was accepted at p < 0.05.Participant characteristics are reported in Table abnormal sensation in the throat, phlegm and mucous in the throat, tickle and irritation in the throat and a tickle in the throat .The items Discriminant validity was assessed by comparing mean scores between each patient group, and healthy controls, for the final 14-item questionnaire Table . These rConcurrent validity was examined by comparing results to the Leicester Cough Questionnaire and the John Hunter Hospital Symptom and Frequency Severity Questionnaire. The Pearson Correlation Coefficient showed a correlation between the Laryngeal Hypersensitivity Questionnaire the Leicester Cough Questionnaire of .673 (p < .001) and the John Hunter Hospital Symptom Frequency and Severity questionnaire of –.791 (p < .001).Participant characteristics for the responsiveness analysis are reported in Table The Newcastle Laryngeal Hypersensitivity Questionnaire (LHQ) is a valid measure of laryngeal discomfort for patients with laryngeal hypersensitivity syndromes. The final version contains 14 items with a 7 point Likert frequency response scale. It is designed for self-administration and takes less than 5 minutes for completion. The questionnaire was useful in discriminating between patients with laryngeal hypersensitivity syndromes and healthy controls, and was able to detect a change in laryngeal hypersensitivity after speech pathology treatment.Healthy controls had a mean total score of 19.2 (SD = 0.7). A cut off for normal function could be considered to be 17.1 (i.e. mean minus 3 standard deviations). Questionnaire scoring is in a similar direction to the Leicester Cough Questionnaire. Subscale scores are averaged from the number of completed items for each subscale and range from 1 (worst) to 7 (best). The total score is the sum of the three subscale scores which range from 3 (worst) to 21 (best). We calculated the minimal important difference as 1.7 using both a standard statistical approach (at 0.5sd), and as the change in LHQ that corresponded to the MID for the Leicester Cough Questionnaire.The LHQ has a number of potential purposes. It could be used to quantify the patient experience of laryngeal discomfort and to measure change over time. It has the potential to discriminate between patient groups and healthy controls. It could also be used in be used in trials of speech pathology intervention for these clinical groups.most of the time although the quality of the sensation is not the same as in chronic pain. It would appear that the laryngeal sensation is similar between clinical groups and may suggest some underlying sensory neuropathy. These findings are consistent with results of quantitative sensory testing in patients with laryngeal hypersensitivity syndrome [This data also demonstrated that most patients with laryngeal dysfunction have abnormal laryngeal sensation at least syndrome .an abnormal sensation in my throat’, ‘pain in my throat’, and ‘my throat feels tight’. It was beyond the scope of this study to explain causality of symptoms. Although patients had received prior treatment for associated medical conditions such as gastroesophageal reflux disease, asthma, or rhinitis, it is possible that these conditions were contributing to the symptoms. The purpose of the questionnaire was to measure the patient experience of laryngeal symptoms rather than determine the causality of symptoms.Neural hypersensitivity is best characterised in chronic pain syndromes. Symptoms indicating hypersensitivity include a spontaneously occurring sensation, termed pesthesia, increased perception of pain for a given stimulus level, termed hyperalgesia, and a situation where a normally non-painful stimulus evokes pain, termed allodynia. There is growing recognition that laryngeal symptoms in chronic cough can be interpreted in a similar fashion ,8. ThereWhen coupled with a history that these symptoms develop with nontussive triggers , or as an exaggerated response to stimuli (hypertussia), the LHQ can aid in the recognition of a laryngeal hypersensitivity syndrome with central sensitisation. This has important treatment implications as recent treatment developments successfully apply the treatment approaches used in chronic pain to chronic refractory cough, such as behavioural therapy  or gabapThese concepts can be also applied to other laryngeal hypersensitivity syndromes, such as PVFM, muscle tension dysphonia, and globus. We have recently reported evidence for laryngeal pesthesia in these conditions  as well One potential limitation of this study is the small sample size for some of the disease groups. This can be overcome by future research that assesses the LHQ in muscle tension dysphonia and globus. The sample size used reflected the referral patterns and community prevalence of these conditions. The patient mix, while heterogeneous, was reflective of overlapping symptomatology and consistent with the multiple underlying medical factors which affect this population. It is possible that this group may not be representative of any particular disorder. Full thematic analysis was not conducted in the item generation phase of the study. Further study of the MID would be useful.In conclusion, the study reports the development and validation of a tool to measure laryngeal hypersensitivity that can readily be applied in clinical practice and research. The LHQ will facilitate the recognition and assessment of laryngeal hypersensitivity in several laryngeal disorders and should be useful in as an outcome measure in clinical trials.1. There is an abnormal sensation in my throat.(circle one)All of the time. 1Most of the time. 2A good bit of the time. 3Some of the time. 4A little of the time. 5Hardly any of the time. 6None of the time. 72. I feel phlegm and mucous in my throat3. I have pain in my throat4. I have a sensation of something stuck in my throat5. My throat is blocked.6. My mouth and/or throat feels dry.7. My throat feels tight.8. There is an irritation in my throat.9. I have a sensation of something pushing on my chest.10. I have a sensation of something pressing on my throat11. There is a feeling of constriction as though needing to inhale a large amount of air.12. Food catches when I eat or drink.13. There is a tickle in my throat.14. There is an itch in my throat.15. I have a tingling sensation in my throat16. I have pins and needles in my throat17. I have a hot or burning sensation in my throat.18. I have numbness in my throat19. I have a sensation of an electric shock in my throat.20. There is a shooting sensation in my throat21. There is a freezing or painfully cold sensation in my throat.John Hunter Hospital Laryngeal pesthesia Questionnaire.1. There is an abnormal sensation in my throat. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 72. I feel phlegm and mucous in my throat (TT)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 73. I have pain in my throat (P/Th)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 74. I have a sensation of something stuck in my throat (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 75. My throat is blocked. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 76. My throat feels tight. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 77. There is an irritation in my throat. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 78. I have a sensation of something pushing on my chest. (P/Th)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the timee……………………………………………… 79. I have a sensation of something pressing on my throat (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time………………………………………………. 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 710. There is a feeling of constriction as though needing to inhale a large amount of air. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 711. Food catches when I eat or drink. (O)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 712. There is a tickle in my throat. (TT)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 713. There is an itch in my throat. (TT)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 714. I have a hot or burning sensation in my throat (P/Th)(circle one)All of the time……………………………………………… 1Most of the time……………………………………………… 2A good bit of the time……………………………………………… 3Some of the time……………………………………………… 4A little of the time……………………………………………… 5Hardly any of the time……………………………………………… 6None of the time……………………………………………… 7LHQ: Laryngeal hypersensitivity questionnaire; PVFM: Paradoxical vocal fold movement.The authors declare that they have no competing interests.AV and PG conceived the study and wrote the manuscript. AV did the statistical analysis. SB was responsible for collection and collation of the data. All authors read and approved the final manuscript.