{"id":"https://openalex.org/W6910691096","doi":"https://doi.org/10.48550/arxiv.2507.10254","title":"Reshetnyak-class mappings and composition operators","display_name":"Reshetnyak-class mappings and composition operators","publication_year":2025,"publication_date":"2025-07-14","ids":{"openalex":"https://openalex.org/W6910691096","doi":"https://doi.org/10.48550/arxiv.2507.10254"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2507.10254","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.10254","pdf_url":"https://arxiv.org/pdf/2507.10254","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2507.10254","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"V., Pavlov S.","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V., Pavlov S.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"K, Vodopyanov S.","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K, Vodopyanov S.","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":false,"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":true,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.4413999915122986,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.4413999915122986,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.334199994802475,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.08460000157356262,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/composition-operators","display_name":"composition operators","score":0.9810000061988831},{"id":"https://openalex.org/keywords/carnot-groups","display_name":"Carnot groups","score":0.9520000219345093},{"id":"https://openalex.org/keywords/homogeneous-sobolev-spaces","display_name":"homogeneous Sobolev spaces","score":0.859000027179718},{"id":"https://openalex.org/keywords/bounded-composition-operators","display_name":"bounded composition operators","score":0.6100000143051147},{"id":"https://openalex.org/keywords/lipschitz-functions","display_name":"Lipschitz functions","score":0.722000002861023}],"concepts":[{"id":"https://openalex.org/C119104473","wikidata":"https://www.wikidata.org/wiki/Q188910","display_name":"Carnot cycle","level":2,"score":0.9409000277519226},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7871000170707703},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7689999938011169},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.597100019454956},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5667999982833862},{"id":"https://openalex.org/C40231798","wikidata":"https://www.wikidata.org/wiki/Q1333743","display_name":"Composition (language)","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5394999980926514},{"id":"https://openalex.org/C21513729","wikidata":"https://www.wikidata.org/wiki/Q5156798","display_name":"Composition operator","level":4,"score":0.49059998989105225},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.4023999869823456},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38350000977516174},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C24250787","wikidata":"https://www.wikidata.org/wiki/Q7269510","display_name":"Quasinormal operator","level":4,"score":0.27489998936653137},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2507.10254","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.10254","pdf_url":"https://arxiv.org/pdf/2507.10254","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.2507.10254","doi":"https://doi.org/10.48550/arxiv.2507.10254","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.10254","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2507.10254","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.10254","pdf_url":"https://arxiv.org/pdf/2507.10254","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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"the":[1,22,26,46,53,65,94,110],"Reshetnyak-class":[2],"homeomorphisms":[3,54,111],"$\u03c6:\u03a9\\to":[4],"Y$,":[5],"where~$\u03a9$":[6],"is":[7,14,90],"a~domain":[8],"in":[9,58,112],"some":[10,59],"Carnot":[11,60],"group":[12],"and~$Y$":[13],"a~metric":[15],"space,":[16],"we":[17],"obtain":[18,106],"an~equivalent":[19],"description":[20],"as":[21,39],"mappings":[23],"which":[24,63],"induce":[25,64],"bounded":[27,66],"composition":[28,67],"operator":[29,68],"$$":[30,34,69,82],"\u03c6^*:{\\rm":[31],"Lip}(Y)\\to":[32],"L_q^1(\u03a9),":[33],"where":[35],"$1\\leq":[36],"q\\leq":[37],"\\infty$,":[38],"$\u03c6^*u=u\\circ\u03c6$":[40],"for":[41],"$u\\in{\\rm":[42],"Lip}(Y)$.":[43],"We":[44],"demonstrate":[45],"utility":[47],"of":[48,56,83,100,109],"our":[49],"approach":[50],"by":[51],"characterizing":[52],"$\u03c6:\u03a9\\to\u03a9'$":[55],"domains":[57],"group~$\\mathbb":[61],"G$":[62],"\u03c6^*:":[70],"L^1_p(\u03a9')\\cap":[71],"{\\rm":[72],"Lip}_{\\rm":[73],"loc}(\u03a9')\\to":[74],"L^1_q":[75],"(\u03a9),\\quad":[76],"1\\leq":[77],"q":[78],"\\leq":[79],"p\\leq":[80],"\\infty,":[81],"homogeneous":[84],"Sobolev":[85],"spaces.":[86],"The":[87],"new":[88,107],"proof":[89],"much":[91],"shorter":[92],"than":[93],"one":[95],"already":[96],"available,":[97],"requires":[98],"a~minimum":[99],"tools,":[101],"and":[102],"enables":[103],"us":[104],"to":[105],"properties":[108],"question.":[113]},"counts_by_year":[],"updated_date":"2026-09-25T08:18:29.962427","created_date":"2025-10-10T00:00:00"}