{"id":"https://openalex.org/W3018912323","doi":"https://doi.org/10.1080/00029890.2020.1718953","title":"Riesz\u2019s Theorem for Lumer\u2019s Hardy Spaces","display_name":"Riesz\u2019s Theorem for Lumer\u2019s Hardy Spaces","publication_year":2020,"publication_date":"2020-04-23","ids":{"openalex":"https://openalex.org/W3018912323","doi":"https://doi.org/10.1080/00029890.2020.1718953","mag":"3018912323"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1718953","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1718953","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029511307","display_name":"Marijan Markovi\u0107","orcid":"https://orcid.org/0000-0002-8711-3328"},"institutions":[{"id":"https://openalex.org/I5936373","display_name":"University of Montenegro","ror":"https://ror.org/02drrjp49","country_code":"ME","type":"education","lineage":["https://openalex.org/I5936373"]}],"countries":["ME"],"is_corresponding":true,"raw_author_name":"Marijan Markovi\u0107","raw_affiliation_strings":["Faculty of Sciences and Mathematics, University of Montenegro, D\u017eord\u017ea Va\u0161ingtona bb, 81000 Podgorica, Montenegro"],"affiliations":[{"raw_affiliation_string":"Faculty of Sciences and Mathematics, University of Montenegro, D\u017eord\u017ea Va\u0161ingtona bb, 81000 Podgorica, Montenegro","institution_ids":["https://openalex.org/I5936373"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029511307"],"corresponding_institution_ids":["https://openalex.org/I5936373"],"apc_list":null,"apc_paid":null,"fwci":0.2915,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.45956868,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"127","issue":"5","first_page":"452","last_page":"455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9990000128746033,"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":0.9990000128746033,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9926999807357788,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9842000007629395,"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/mathematics","display_name":"Mathematics","score":0.7761982679367065},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.750773549079895},{"id":"https://openalex.org/keywords/riesz-transform","display_name":"Riesz transform","score":0.7380434274673462},{"id":"https://openalex.org/keywords/hardy-space","display_name":"Hardy space","score":0.7091725468635559},{"id":"https://openalex.org/keywords/riesz-representation-theorem","display_name":"Riesz representation theorem","score":0.6882593035697937},{"id":"https://openalex.org/keywords/conjugate","display_name":"Conjugate","score":0.6542367935180664},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6131876707077026},{"id":"https://openalex.org/keywords/riesz-potential","display_name":"Riesz potential","score":0.528806209564209},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48301658034324646},{"id":"https://openalex.org/keywords/m.-riesz-extension-theorem","display_name":"M. Riesz extension theorem","score":0.46590572595596313},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4583854079246521},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.4425419270992279},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11292743682861328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7761982679367065},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.750773549079895},{"id":"https://openalex.org/C82997116","wikidata":"https://www.wikidata.org/wiki/Q7333169","display_name":"Riesz transform","level":2,"score":0.7380434274673462},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.7091725468635559},{"id":"https://openalex.org/C113675457","wikidata":"https://www.wikidata.org/wiki/Q1357684","display_name":"Riesz representation theorem","level":2,"score":0.6882593035697937},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.6542367935180664},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6131876707077026},{"id":"https://openalex.org/C189987565","wikidata":"https://www.wikidata.org/wiki/Q7333166","display_name":"Riesz potential","level":2,"score":0.528806209564209},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48301658034324646},{"id":"https://openalex.org/C56969512","wikidata":"https://www.wikidata.org/wiki/Q3527217","display_name":"M. Riesz extension theorem","level":2,"score":0.46590572595596313},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4583854079246521},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4425419270992279},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11292743682861328},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00029890.2020.1718953","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1718953","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W79434187","https://openalex.org/W1594563152","https://openalex.org/W1995177232","https://openalex.org/W2037612300","https://openalex.org/W2328006128","https://openalex.org/W2332482475","https://openalex.org/W4231485790","https://openalex.org/W4299318877"],"related_works":["https://openalex.org/W2440474188","https://openalex.org/W2949066030","https://openalex.org/W4294755053","https://openalex.org/W3142231895","https://openalex.org/W2892015605","https://openalex.org/W2035270346","https://openalex.org/W2354006822","https://openalex.org/W2073521301","https://openalex.org/W2320555943","https://openalex.org/W2389152991"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3,65],"obtain":[4],"a":[5,26,32,39],"version":[6],"of":[7],"the":[8,62,67,72],"well-known":[9],"Riesz\u2019s":[10],"theorem":[11],"on":[12,21,36,50],"conjugate":[13,34,64],"harmonic":[14,28,33,41],"functions":[15],"for":[16,61],"Lumer\u2019s":[17],"Hardy":[18],"spaces":[19],"(Lh)2(\u03a9)":[20],"arbitrary":[22],"domains":[23],"\u03a9:":[24],"If":[25],"real-valued":[27,40],"function":[29,42],"U\u2208(Lh)2(\u03a9)":[30],"has":[31],"V":[35],"\u03a9":[37],"(i.e.,":[38],"such":[43],"that":[44],"U":[45,53],"+":[46,54],"iV":[47,55],"is":[48],"analytic":[49],"\u03a9),":[51],"then":[52],"also":[56],"belongs":[57],"to":[58],"(Lh)2(\u03a9),":[59],"and":[60],"normalized":[63],"have":[66],"norm":[68],"estimate":[69],"||U+iV||(Lh)2(\u03a9)\u22642||U||(Lh)2(\u03a9),":[70],"with":[71],"best":[73],"possible":[74],"constant.":[75]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
