Characterization of generalized Orlicz spaces

Detalhes bibliográficos
Autor(a) principal: Ferreira, Rita
Data de Publicação: 2020
Outros Autores: Hästö, Peter, Ribeiro, Ana Margarida
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/93389
Resumo: The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.
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spelling Characterization of generalized Orlicz spacesMusielak-Orlicz spacesOrlicz spacePoincaré inequalitySobolev spacevariable exponentMathematics(all)Applied MathematicsThe norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNFerreira, RitaHästö, PeterRibeiro, Ana Margarida2020-02-26T23:37:30Z2020-03-012020-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10362/93389eng0219-1997PURE: 11732575https://doi.org/10.1142/S0219199718500797info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T04:41:45Zoai:run.unl.pt:10362/93389Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:37:43.792670Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Characterization of generalized Orlicz spaces
title Characterization of generalized Orlicz spaces
spellingShingle Characterization of generalized Orlicz spaces
Ferreira, Rita
Musielak-Orlicz spaces
Orlicz space
Poincaré inequality
Sobolev space
variable exponent
Mathematics(all)
Applied Mathematics
title_short Characterization of generalized Orlicz spaces
title_full Characterization of generalized Orlicz spaces
title_fullStr Characterization of generalized Orlicz spaces
title_full_unstemmed Characterization of generalized Orlicz spaces
title_sort Characterization of generalized Orlicz spaces
author Ferreira, Rita
author_facet Ferreira, Rita
Hästö, Peter
Ribeiro, Ana Margarida
author_role author
author2 Hästö, Peter
Ribeiro, Ana Margarida
author2_role author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Ferreira, Rita
Hästö, Peter
Ribeiro, Ana Margarida
dc.subject.por.fl_str_mv Musielak-Orlicz spaces
Orlicz space
Poincaré inequality
Sobolev space
variable exponent
Mathematics(all)
Applied Mathematics
topic Musielak-Orlicz spaces
Orlicz space
Poincaré inequality
Sobolev space
variable exponent
Mathematics(all)
Applied Mathematics
description The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Because the difference quotient is based on shifting the function, it cannot be used in generalized Orlicz spaces. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the generalized Orlicz-Sobolev space. Our results are new even in Orlicz spaces and variable exponent spaces.
publishDate 2020
dc.date.none.fl_str_mv 2020-02-26T23:37:30Z
2020-03-01
2020-03-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/93389
url http://hdl.handle.net/10362/93389
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0219-1997
PURE: 11732575
https://doi.org/10.1142/S0219199718500797
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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