{"id":"https://openalex.org/W7223134332","doi":"https://doi.org/10.3390/math14203824","title":"Exact Norms and Morrey Estimates for Logarithmic Hardy Operators and Their Commutators on the Half-Line","display_name":"Exact Norms and Morrey Estimates for Logarithmic Hardy Operators and Their Commutators on the Half-Line","publication_year":2026,"publication_date":"2026-10-21","ids":{"openalex":"https://openalex.org/W7223134332","doi":"https://doi.org/10.3390/math14203824"},"language":"en","primary_location":{"id":"doi:10.3390/math14203824","doi":"https://doi.org/10.3390/math14203824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14203824","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math14203824","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064689073","display_name":"Francis Mora-Ferreras","orcid":"https://orcid.org/0000-0002-8050-5871","observed_orcids":["https://orcid.org/0000-0002-8050-5871"]},"institutions":[{"id":"https://openalex.org/I154348853","display_name":"Universidad Aut\u00f3noma de Santo Domingo","ror":"https://ror.org/05478zz46","country_code":"DO","type":"education","lineage":["https://openalex.org/I154348853"]},{"id":"https://openalex.org/I4210117065","display_name":"Universidad Nacional Pedro Henr\u00edquez Ure\u00f1a","ror":"https://ror.org/03ad1cn37","country_code":"DO","type":"education","lineage":["https://openalex.org/I4210117065"]}],"countries":["DO"],"is_corresponding":true,"raw_author_name":"Francis Mora-Ferreras","raw_affiliation_strings":["Departamento de Matem\u00e1tica y Estad\u00edstica, Universidad Nacional Pedro Henr\u00edquez Ure\u00f1a, Santo Domingo 1423, Dominican Republic","Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica y Estad\u00edstica, Universidad Nacional Pedro Henr\u00edquez Ure\u00f1a, Santo Domingo 1423, Dominican Republic","institution_ids":["https://openalex.org/I4210117065"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic","institution_ids":["https://openalex.org/I154348853"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159161198","display_name":"Manuel Montero","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154348853","display_name":"Universidad Aut\u00f3noma de Santo Domingo","ror":"https://ror.org/05478zz46","country_code":"DO","type":"education","lineage":["https://openalex.org/I154348853"]}],"countries":["DO"],"is_corresponding":false,"raw_author_name":"Manuel Montero","raw_affiliation_strings":["Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic","institution_ids":["https://openalex.org/I154348853"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5159192622","display_name":"Victor Ram\u00edrez","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154348853","display_name":"Universidad Aut\u00f3noma de Santo Domingo","ror":"https://ror.org/05478zz46","country_code":"DO","type":"education","lineage":["https://openalex.org/I154348853"]}],"countries":["DO"],"is_corresponding":false,"raw_author_name":"Victor Ram\u00edrez","raw_affiliation_strings":["Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica, Facultad de Ciencias, Universidad Aut\u00f3noma de Santo Domingo, Santo Domingo 1356, Dominican Republic","institution_ids":["https://openalex.org/I154348853"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064689073"],"corresponding_institution_ids":["https://openalex.org/I154348853","https://openalex.org/I4210117065"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.73803655,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"20","first_page":"3824","last_page":"3824"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.9980000257492065,"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":0.9980000257492065,"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":0.0006000000284984708,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.00039999998989515007,"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/commutators","display_name":"commutators","score":0.9419999718666077},{"id":"https://openalex.org/keywords/morrey-spaces","display_name":"Morrey spaces","score":0.9829999804496765},{"id":"https://openalex.org/keywords/rays","display_name":"rays","score":0.8569999933242798},{"id":"https://openalex.org/keywords/reverse-inequalities","display_name":"reverse inequalities","score":0.6729999780654907},{"id":"https://openalex.org/keywords/fractional-operators","display_name":"fractional operators","score":0.5950000286102295},{"id":"https://openalex.org/keywords/mapping-theorems","display_name":"mapping theorems","score":0.7200000286102295},{"id":"https://openalex.org/keywords/commutator-estimates","display_name":"commutator estimates","score":0.6489999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8894000053405762},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6330000162124634},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5964999794960022},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5867000222206116},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5555999875068665},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5146999955177307},{"id":"https://openalex.org/C145620117","wikidata":"https://www.wikidata.org/wiki/Q2989763","display_name":"Commutator","level":4,"score":0.5123000144958496},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5041000247001648},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4733999967575073},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C42178598","wikidata":"https://www.wikidata.org/wiki/Q1585233","display_name":"Hardy space","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.3571000099182129},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3395000100135803},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28119999170303345},{"id":"https://openalex.org/C139907963","wikidata":"https://www.wikidata.org/wiki/Q198740","display_name":"Law of the iterated logarithm","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25780001282691956},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/math14203824","doi":"https://doi.org/10.3390/math14203824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14203824","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:61bd5d260b264622b343bb4df98cc706","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/61bd5d260b264622b343bb4df98cc706","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 14, Iss 20, p 3824 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math14203824","doi":"https://doi.org/10.3390/math14203824","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math14203824","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1602368396","https://openalex.org/W1973089024","https://openalex.org/W1977307083","https://openalex.org/W1988212859","https://openalex.org/W2001657683","https://openalex.org/W2046582302","https://openalex.org/W2068783037","https://openalex.org/W2088463128","https://openalex.org/W2121132354","https://openalex.org/W2286769289","https://openalex.org/W2948715070","https://openalex.org/W2962953231","https://openalex.org/W2972793635","https://openalex.org/W2996993439","https://openalex.org/W3036627574","https://openalex.org/W4230410641","https://openalex.org/W4243436364","https://openalex.org/W4289015086","https://openalex.org/W4408380124","https://openalex.org/W4409542001","https://openalex.org/W4410859678"],"related_works":["https://openalex.org/W7222971048","https://openalex.org/W4415271725","https://openalex.org/W2202753798","https://openalex.org/W3011212106","https://openalex.org/W2068783037","https://openalex.org/W2121132354","https://openalex.org/W2973061821","https://openalex.org/W4229366289","https://openalex.org/W2364020996","https://openalex.org/W2032357640"],"abstract_inverted_index":{"We":[0,37,87],"study":[1],"logarithmic":[2,77,129,139],"Hardy":[3,42],"operators":[4],"and":[5,21,44,70,108,112,130,143],"their":[6],"commutators":[7],"on":[8],"the":[9,23,28,53,66,93,98,117,138,151],"half-line":[10],"Morrey":[11,63],"spaces":[12,111],"defined":[13],"using":[14],"all":[15],"bounded":[16],"intervals.":[17],"For":[18,52,97],"1\u2264p<\u221e,":[19],"0<\u03bb<1,":[20],"\u03b3>\u22121,":[22],"positive":[24],"dilation":[25],"principle":[26],"gives":[27,144],"exact":[29,39,146],"norm":[30,148],"\u0393(\u03b3+1)[p/(p+\u03bb\u22121)]\u03b3+1,":[31],"attained":[32],"by":[33,141],"a":[34,45,58,76],"power":[35],"function.":[36],"obtain":[38],"norms":[40],"for":[41,48,82],"iterates":[43],"reverse":[46],"inequality":[47],"nonnegative":[49],"nonincreasing":[50],"functions.":[51],"fractional":[54,131],"operator,":[55],"we":[56,103],"prove":[57,104],"mapping":[59,95],"theorem":[60],"between":[61],"distinct":[62],"spaces,":[64],"establish":[65],"necessary":[67],"scaling":[68],"relation,":[69],"give":[71],"explicit":[72,128],"upper":[73,153],"bounds":[74],"throughout":[75],"range":[78],"that":[79],"is":[80],"optimal":[81],"finiteness":[83],"at":[84],"every":[85],"point.":[86],"distinguish":[88],"this":[89],"pointwise":[90],"threshold":[91],"from":[92],"almost-everywhere":[94],"endpoint.":[96],"one-sided":[99],"point-value":[100,119],"symbol":[101,125,135],"class,":[102],"embeddings":[105],"into":[106],"ordinary":[107],"central":[109],"mean-oscillation":[110],"identify":[113],"its":[114],"relation":[115],"to":[116],"symmetric":[118],"class":[120],"through":[121],"even":[122],"extension.":[123],"This":[124],"condition":[126],"yields":[127],"commutator":[132,147],"estimates.":[133],"The":[134],"b(x)=logx":[136],"raises":[137],"order":[140],"one":[142],"an":[145],"with":[149],"which":[150],"general":[152],"bound":[154],"can":[155],"be":[156],"compared.":[157]},"counts_by_year":[],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2026-10-22T00:00:00"}
