{"id":"https://openalex.org/W7214029310","doi":"https://doi.org/10.48550/arxiv.2609.22898","title":"Campanato spaces via quantum semigroups","display_name":"Campanato spaces via quantum semigroups","publication_year":2026,"publication_date":"2026-09-19","ids":{"openalex":"https://openalex.org/W7214029310","doi":"https://doi.org/10.48550/arxiv.2609.22898"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.22898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22898","pdf_url":"https://arxiv.org/pdf/2609.22898","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/2609.22898","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053148333","display_name":"Guixiang Hong","orcid":"https://orcid.org/0000-0002-1467-3180","observed_orcids":["https://orcid.org/0000-0002-1467-3180"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong, Guixiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020166715","display_name":"Yuanyuan Jing","orcid":"https://orcid.org/0000-0003-4932-8712","observed_orcids":["https://orcid.org/0000-0003-4932-8712"]},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing, Yuanyuan","raw_affiliation_strings":["Institute for Advanced Study in Mathematics , Harbin Institute of Technology , 150001 , Harbin , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Advanced Study in Mathematics , Harbin Institute of Technology , 150001 , Harbin , P.R. China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152451243","display_name":"Ping Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I43922553","display_name":"Wuhan University of Science and Technology","ror":"https://ror.org/00e4hrk88","country_code":"CN","type":"education","lineage":["https://openalex.org/I43922553"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Ping","raw_affiliation_strings":["School of Mathematics and Systems Science , and Center for Mathematics Sciences , Wuhan University of Science and Technology , 430065 , Wuhan , P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Systems Science , and Center for Mathematics Sciences , Wuhan University of Science and Technology , 430065 , Wuhan , P.R. China","institution_ids":["https://openalex.org/I43922553"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.4966000020503998,"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":0.4966000020503998,"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":0.26899999380111694,"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"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.20579999685287476,"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/campanato-spaces","display_name":"Campanato spaces","score":1.0},{"id":"https://openalex.org/keywords/quantum-semigroups","display_name":"quantum semigroups","score":0.8920000195503235},{"id":"https://openalex.org/keywords/analytic-semigroups","display_name":"analytic semigroups","score":0.8820000290870667},{"id":"https://openalex.org/keywords/von-neumann-algebras","display_name":"von Neumann algebras","score":0.9760000109672546},{"id":"https://openalex.org/keywords/lipschitz-spaces","display_name":"Lipschitz spaces","score":0.9300000071525574},{"id":"https://openalex.org/keywords/self-improving-properties","display_name":"self-improving properties","score":0.9150000214576721},{"id":"https://openalex.org/keywords/noncommutative-harmonic-analysis","display_name":"noncommutative harmonic analysis","score":0.7070000171661377}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7699000239372253},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.652400016784668},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5853999853134155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5748999714851379},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.46540001034736633},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4343000054359436},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32580000162124634},{"id":"https://openalex.org/C137343772","wikidata":"https://www.wikidata.org/wiki/Q584910","display_name":"Neumann series","level":2,"score":0.3240000009536743},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3012999892234802},{"id":"https://openalex.org/C46149467","wikidata":"https://www.wikidata.org/wiki/Q7574800","display_name":"Special classes of semigroups","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.22898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22898","pdf_url":"https://arxiv.org/pdf/2609.22898","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.2609.22898","doi":"https://doi.org/10.48550/arxiv.2609.22898","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.22898","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:2609.22898","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.22898","pdf_url":"https://arxiv.org/pdf/2609.22898","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/G2054192911","display_name":null,"funder_award_id":"12031004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5343799843","display_name":null,"funder_award_id":"12325105","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5572799011","display_name":null,"funder_award_id":"12071355","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7944262688","display_name":null,"funder_award_id":"W2441002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G918430532","display_name":null,"funder_award_id":"12371136","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320323173","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214029310.pdf","grobid_xml":"https://content.openalex.org/works/W7214029310.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4403002368","https://openalex.org/W2962919371","https://openalex.org/W1000986257","https://openalex.org/W2124121640","https://openalex.org/W4247217495","https://openalex.org/W1977825247","https://openalex.org/W1964480920","https://openalex.org/W2963650416","https://openalex.org/W2811042529","https://openalex.org/W2518015328"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,62],"continue":[4],"to":[5,71,102],"investigate":[6],"Campanato":[7,53,67],"spaces":[8,25,54,68],"via":[9],"semigroups":[10,38],"on":[11,39],"von":[12,40],"Neumann":[13,41],"algebras.":[14],"One":[15],"of":[16,52],"the":[17,48,65,72,87,92,99,116,119,125],"main":[18],"results":[19,101,117],"is":[20],"their":[21],"coincidence":[22],"with":[23],"Lipschitz":[24],"for":[26,34,75],"{\\it":[27,36,43,76],"all}":[28,77],"regularity":[29],"indices":[30],"$\u03b1>":[31,78],"0$":[32],"and":[33,106,118],"all":[35],"analytic}":[37],"algebras":[42],"not":[44,81],"necessarily":[45],"being":[46],"finite};":[47],"desired":[49],"self-improving":[50],"property":[51],"has":[55],"also":[56,97],"been":[57],"verified.":[58],"As":[59],"a":[60],"consequence,":[61],"demonstrate":[63],"that":[64],"column":[66],"are":[69,121],"isomorphic":[70],"row":[73],"ones":[74],"0$.":[79],"This":[80],"only":[82],"removes":[83],"several":[84,109],"restrictions":[85],"in":[86,113,124],"previous":[88,100],"work":[89],"\\cite{HJ24}":[90],"by":[91],"first":[93],"two":[94],"authors,":[95],"but":[96],"extends":[98],"any":[103],"analytic":[104],"semigroup,":[105],"thus":[107],"resolves":[108],"problems":[110],"left":[111],"open":[112],"\\cite{HJ24}.":[114],"Both":[115],"proof":[120],"new":[122],"even":[123],"commutative":[126],"setting.":[127]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-23T00:00:00"}