{"id":"https://openalex.org/W7213290730","doi":"https://doi.org/10.48550/arxiv.2609.14298","title":"Non-radial Dunkl multipliers at the $L^2$-Sobolev threshold","display_name":"Non-radial Dunkl multipliers at the $L^2$-Sobolev threshold","publication_year":2026,"publication_date":"2026-09-13","ids":{"openalex":"https://openalex.org/W7213290730","doi":"https://doi.org/10.48550/arxiv.2609.14298"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.14298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14298","pdf_url":"https://arxiv.org/pdf/2609.14298","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.14298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151822430","display_name":"Der-Chen Chang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Der-Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151779227","display_name":"Ji Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ji","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034661323","display_name":"Chaojie Wen","orcid":"https://orcid.org/0009-0009-4889-2902","observed_orcids":["https://orcid.org/0009-0009-4889-2902"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen, Chaojie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068709599","display_name":"Liangchuan Wu","orcid":"https://orcid.org/0000-0003-2423-1690","observed_orcids":["https://orcid.org/0000-0003-2423-1690"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Liangchuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9086999893188477,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9086999893188477,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.08649999648332596,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dunkl-transform","display_name":"Dunkl transform","score":0.8999999761581421},{"id":"https://openalex.org/keywords/finite-reflection-groups","display_name":"finite reflection groups","score":0.8389999866485596},{"id":"https://openalex.org/keywords/homogeneous-dimension","display_name":"homogeneous dimension","score":0.5339999794960022},{"id":"https://openalex.org/keywords/hardy-spaces","display_name":"Hardy spaces","score":0.4269999861717224},{"id":"https://openalex.org/keywords/lp-boundedness","display_name":"Lp boundedness","score":0.6579999923706055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.823199987411499},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.7185999751091003},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5353000164031982},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.5236999988555908},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47269999980926514},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35499998927116394},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3253999948501587},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.23720000684261322}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.14298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14298","pdf_url":"https://arxiv.org/pdf/2609.14298","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.14298","doi":"https://doi.org/10.48550/arxiv.2609.14298","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.14298","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.14298","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.14298","pdf_url":"https://arxiv.org/pdf/2609.14298","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G184354734","display_name":null,"funder_award_id":"#12201002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G666339264","display_name":"Intrinsic structures in partial differential equations","funder_award_id":"DP260100485","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213290730.pdf","grobid_xml":"https://content.openalex.org/works/W7213290730.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7140200765","https://openalex.org/W7163126695","https://openalex.org/W7167236775"],"related_works":["https://openalex.org/W7213527999","https://openalex.org/W2013713977","https://openalex.org/W4407084280","https://openalex.org/W4289762365","https://openalex.org/W2821104895","https://openalex.org/W7140200765","https://openalex.org/W1998661538","https://openalex.org/W4405661847","https://openalex.org/W2203528358","https://openalex.org/W2086404182"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,26],"H\u00f6rmander":[3],"multiplier":[4],"theorem":[5],"for":[6,20,41],"the":[7,21,35],"Dunkl":[8],"transform":[9],"associated":[10],"with":[11,29],"an":[12],"arbitrary":[13],"finite":[14],"reflection":[15],"group.":[16],"Uniform":[17],"$H^\u03c3(\\mathbb{R}^N)$":[18],"bounds":[19],"normalised":[22],"dyadic":[23],"pieces":[24],"of":[25],"measurable":[27],"symbol,":[28],"$\u03c3>\\mathbf":[30],"N/2$":[31],"and":[32],"$\\mathbf":[33],"N$":[34],"homogeneous":[36],"dimension,":[37],"imply":[38],"$L^p(d\u03c9)$":[39],"boundedness":[40],"$1":[42]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}