{"id":"https://openalex.org/W2142212561","doi":"https://doi.org/10.2478/v10037-010-0018-6","title":"On Lp Space Formed by Real-Valued Partial Functions","display_name":"On Lp Space Formed by Real-Valued Partial Functions","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2142212561","doi":"https://doi.org/10.2478/v10037-010-0018-6","mag":"2142212561"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-010-0018-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-010-0018-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.2478/v10037-010-0018-6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070513311","display_name":"Yasushige Watase","orcid":null},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasushige Watase","raw_affiliation_strings":["[Graduate School of Science and Technology, Shinshu University, Nagano, Japan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Graduate School of Science and Technology, Shinshu University, Nagano, Japan]","institution_ids":["https://openalex.org/I137975476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015450295","display_name":"Noboru Endou","orcid":"https://orcid.org/0000-0002-5922-2332"},"institutions":[{"id":"https://openalex.org/I4210113483","display_name":"National Institute of Technology, Gifu College","ror":"https://ror.org/025b2hx26","country_code":"JP","type":"education","lineage":["https://openalex.org/I4210113483","https://openalex.org/I4210120810"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Noboru Endou","raw_affiliation_strings":["Gifu National College of Technology, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Gifu National College of Technology, Japan","institution_ids":["https://openalex.org/I4210113483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055549852","display_name":"Yasunari Shidama","orcid":"https://orcid.org/0000-0001-5634-0838"},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yasunari Shidama","raw_affiliation_strings":["[Shinshu Univ., Nagano, Japan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[Shinshu Univ., Nagano, Japan]","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7962,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.7061144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"18","issue":"3","first_page":"159","last_page":"169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9970999956130981,"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"}},"topics":[{"id":"https://openalex.org/T11545","display_name":"Advanced Banach Space Theory","score":0.9970999956130981,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.963100016117096,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9610000252723694,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7154958248138428},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.6989797949790955},{"id":"https://openalex.org/keywords/minkowski-inequality","display_name":"Minkowski inequality","score":0.6988053917884827},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.6435189843177795},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.573647141456604},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.571456253528595},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5538057684898376},{"id":"https://openalex.org/keywords/besov-space","display_name":"Besov space","score":0.50872403383255},{"id":"https://openalex.org/keywords/locally-integrable-function","display_name":"Locally integrable function","score":0.4721560478210449},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4500378966331482},{"id":"https://openalex.org/keywords/square-integrable-function","display_name":"Square-integrable function","score":0.4474402666091919},{"id":"https://openalex.org/keywords/partial-function","display_name":"Partial function","score":0.413920134305954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40824705362319946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.28027039766311646},{"id":"https://openalex.org/keywords/interpolation-space","display_name":"Interpolation space","score":0.2668952941894531},{"id":"https://openalex.org/keywords/h\u00f6lders-inequality","display_name":"H\u00f6lder's inequality","score":0.23411959409713745},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.2018842101097107},{"id":"https://openalex.org/keywords/functional-analysis","display_name":"Functional analysis","score":0.15169835090637207},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.11780810356140137},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.0750664472579956},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07388710975646973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7154958248138428},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.6989797949790955},{"id":"https://openalex.org/C102379996","wikidata":"https://www.wikidata.org/wiki/Q755092","display_name":"Minkowski inequality","level":5,"score":0.6988053917884827},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.6435189843177795},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.573647141456604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.571456253528595},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5538057684898376},{"id":"https://openalex.org/C129698243","wikidata":"https://www.wikidata.org/wiki/Q526261","display_name":"Besov space","level":5,"score":0.50872403383255},{"id":"https://openalex.org/C83295520","wikidata":"https://www.wikidata.org/wiki/Q1318586","display_name":"Locally integrable function","level":3,"score":0.4721560478210449},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4500378966331482},{"id":"https://openalex.org/C75413324","wikidata":"https://www.wikidata.org/wiki/Q1530791","display_name":"Square-integrable function","level":2,"score":0.4474402666091919},{"id":"https://openalex.org/C182359184","wikidata":"https://www.wikidata.org/wiki/Q1756942","display_name":"Partial function","level":2,"score":0.413920134305954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40824705362319946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28027039766311646},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.2668952941894531},{"id":"https://openalex.org/C91558832","wikidata":"https://www.wikidata.org/wiki/Q731894","display_name":"H\u00f6lder's inequality","level":4,"score":0.23411959409713745},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2018842101097107},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.15169835090637207},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.11780810356140137},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.0750664472579956},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07388710975646973},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10037-010-0018-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-010-0018-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:86b3afda-d592-4c28-8e64-0afed7479f02/oai:repozytorium.uwb.edu.pl:11320/3570","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401248","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:doaj.org/article:3ceac704393e48089a775ef04ea417ed","is_oa":false,"landing_page_url":"https://doaj.org/article/3ceac704393e48089a775ef04ea417ed","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,"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":"Formalized Mathematics, Vol 18, Iss 3, Pp 159-169 (2010)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3570","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/3570","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-010-0018-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-010-0018-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.47999998927116394,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W66860599","https://openalex.org/W68895216","https://openalex.org/W118985555","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W1527353349","https://openalex.org/W1594563152","https://openalex.org/W1619732349","https://openalex.org/W1986609367","https://openalex.org/W2096867974","https://openalex.org/W2098464720","https://openalex.org/W2099252149","https://openalex.org/W2104233978","https://openalex.org/W2105559527","https://openalex.org/W2112482246","https://openalex.org/W2113575928","https://openalex.org/W2114890787","https://openalex.org/W2117761297","https://openalex.org/W2118242375","https://openalex.org/W2123536992","https://openalex.org/W2133273583","https://openalex.org/W2134057927","https://openalex.org/W2134234040","https://openalex.org/W2136691368","https://openalex.org/W2143248787","https://openalex.org/W2150348213","https://openalex.org/W2154026104","https://openalex.org/W2154242071","https://openalex.org/W2159772409","https://openalex.org/W2163011897","https://openalex.org/W2163641194","https://openalex.org/W2186569492","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W2504160609","https://openalex.org/W2547540153","https://openalex.org/W2552817710","https://openalex.org/W4242450648","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4388184466","https://openalex.org/W2065369027","https://openalex.org/W121460163","https://openalex.org/W4300926224","https://openalex.org/W2046837658","https://openalex.org/W2805710756","https://openalex.org/W2607331352","https://openalex.org/W2083713868","https://openalex.org/W2046308441","https://openalex.org/W2142212561"],"abstract_inverted_index":{"On":[0],"L":[1,21,46,52,64],"p":[2,22,38,47,53,65],"Space":[3],"Formed":[4],"by":[5],"Real-Valued":[6],"Partial":[7],"Functions":[8],"This":[9],"article":[10],"is":[11,41,67],"the":[12,18,26,37,51],"continuation":[13],"of":[14,20,28],"[31].":[15],"We":[16,43,55],"define":[17],"set":[19,27],"integrable":[23,48],"functions":[24,31,49],"-":[25],"all":[29],"partial":[30],"whose":[32],"absolute":[33],"value":[34],"raised":[35],"to":[36],"-th":[39],"power":[40],"integrable.":[42],"show":[44],"that":[45,63],"form":[50],"space.":[54],"also":[56],"prove":[57],"Minkowski's":[58],"inequality,":[59],"H\u00f6lder's":[60],"inequality":[61],"and":[62],"space":[66,69],"Banach":[68],"([15],":[70],"[27]).":[71]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
