{"id":"https://openalex.org/W7214017522","doi":"https://doi.org/10.48550/arxiv.2609.23662","title":"Endpoint estimates for commutators of singular integral operators associated with admissible functions","display_name":"Endpoint estimates for commutators of singular integral operators associated with admissible functions","publication_year":2026,"publication_date":"2026-09-20","ids":{"openalex":"https://openalex.org/W7214017522","doi":"https://doi.org/10.48550/arxiv.2609.23662"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23662","pdf_url":"https://arxiv.org/pdf/2609.23662","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/2609.23662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004831222","display_name":"The Anh Bui","orcid":"https://orcid.org/0000-0003-2793-296X","observed_orcids":["https://orcid.org/0000-0003-2793-296X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bui, The Anh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063307120","display_name":"Xuan Thinh Duong","orcid":"https://orcid.org/0000-0002-1123-3745","observed_orcids":["https://orcid.org/0000-0002-1123-3745"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Duong, Xuan Thinh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077690287","display_name":"Luong Dang Ky","orcid":"https://orcid.org/0000-0001-5538-0854","observed_orcids":["https://orcid.org/0000-0001-5538-0854"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ky, Luong Dang","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":0,"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":0.9994999766349792,"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":0.9994999766349792,"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":9.999999747378752e-05,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.0,"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/admissible-functions","display_name":"admissible functions","score":0.8880000114440918},{"id":"https://openalex.org/keywords/spaces-of-homogeneous-type","display_name":"spaces of homogeneous type","score":0.9670000076293945},{"id":"https://openalex.org/keywords/endpoint-estimates","display_name":"endpoint estimates","score":0.8159999847412109},{"id":"https://openalex.org/keywords/schrodinger-operators","display_name":"Schr\u00f6dinger operators","score":0.8169999718666077},{"id":"https://openalex.org/keywords/stratified-lie-groups","display_name":"stratified Lie groups","score":0.996999979019165},{"id":"https://openalex.org/keywords/laguerre-operators","display_name":"Laguerre operators","score":0.8980000019073486},{"id":"https://openalex.org/keywords/convolution-operators","display_name":"convolution operators","score":0.6740000247955322}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8777999877929688},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.822700023651123},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5324000120162964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5232999920845032},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.5066999793052673},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.5005999803543091},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.4708000123500824},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.4700999855995178},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4462999999523163},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44130000472068787},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4163999855518341},{"id":"https://openalex.org/C108408018","wikidata":"https://www.wikidata.org/wiki/Q1124546","display_name":"Laguerre polynomials","level":2,"score":0.4142000079154968},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C2992640183","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral operators","level":4,"score":0.37770000100135803},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.34950000047683716},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C94950523","wikidata":"https://www.wikidata.org/wiki/Q7524241","display_name":"Singular integral operators of convolution type","level":5,"score":0.2777999937534332},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C94906876","wikidata":"https://www.wikidata.org/wiki/Q1132952","display_name":"Homogeneous function","level":3,"score":0.2596000134944916},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23662","pdf_url":"https://arxiv.org/pdf/2609.23662","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.2609.23662","doi":"https://doi.org/10.48550/arxiv.2609.23662","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23662","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:2609.23662","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23662","pdf_url":"https://arxiv.org/pdf/2609.23662","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/G4165347876","display_name":"M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n trong l\u00fd thuy\u1ebft t\u00edch ph\u00e2n k\u1ef3 d\u1ecb v\u00e0 kh\u00f4ng gian h\u00e0m","funder_award_id":"101.02-2023.09","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214017522.pdf","grobid_xml":"https://content.openalex.org/works/W7214017522.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1680338264"],"related_works":["https://openalex.org/W2050163437","https://openalex.org/W2951417425","https://openalex.org/W2101459829","https://openalex.org/W6999098997","https://openalex.org/W2051042652","https://openalex.org/W2017550191","https://openalex.org/W4386488679","https://openalex.org/W4403690547","https://openalex.org/W2729490636","https://openalex.org/W2351823258"],"abstract_inverted_index":{"Let":[0],"$(\\mathcal":[1],"X,":[2],"d,":[3],"\u03bc)$":[4],"be":[5,14],"a":[6,26,37,52],"space":[7,71,86],"of":[8,29,40,78,100,120,122,138],"homogeneous":[9],"type":[10],"and":[11,51,94,109,135],"let":[12],"$\u03c1$":[13],"an":[15,48],"admissible":[16],"function":[17,53],"on":[18,102,131,149],"$\\mathcal":[19],"X$.":[20],"In":[21],"this":[22,115],"paper,":[23],"we":[24,74],"introduce":[25],"new":[27,144],"class":[28],"singular":[30,123],"integral":[31],"operators":[32,41,130,137,148],"associated":[33,61],"with":[34,62],"$\u03c1$,":[35,63],"including":[36,128],"wide":[38],"range":[39],"arising":[42],"in":[43,125],"harmonic":[44],"analysis.":[45],"For":[46],"such":[47],"operator":[49],"$T$":[50],"$b$":[54],"belonging":[55],"to":[56,116],"suitable":[57],"localized":[58],"$\\mathrm{BMO}$":[59],"spaces":[60],"which":[64],"are":[65,143],"strictly":[66],"larger":[67],"than":[68],"the":[69,76,79,84,98,118],"classical":[70],"$\\mathrm{BMO}(\\mathcal":[72],"X)$,":[73,91,93],"establish":[75],"boundedness":[77,99,119],"commutator":[80],"$[b,":[81],"T]$":[82],"from":[83],"Hardy":[85],"$H^1_\u03c1(\\mathcal":[87,95,103],"X)$":[88,104],"into":[89],"$L^{1,\\infty}(\\mathcal":[90],"$L^1(\\mathcal":[92],"X)$.":[96],"Moreover,":[97],"$[b,T]$":[101],"is":[105],"characterized":[106],"by":[107],"necessary":[108],"sufficient":[110],"conditions.":[111],"We":[112],"then":[113],"apply":[114],"investigate":[117],"commutators":[121],"integrals":[124],"various":[126],"settings,":[127],"Schr\u00f6dinger":[129,147],"stratified":[132],"Lie":[133],"groups":[134],"Laguerre":[136],"convolution":[139],"type.":[140],"Our":[141],"results":[142],"even":[145],"for":[146],"$\\mathbb":[150],"R^n$.":[151]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
