Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type

Detalhes bibliográficos
Autor(a) principal: Karlovich, Alexei
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/117157
Resumo: We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space Lp(·) over a space of homogeneous type (X, d, µ) if and only if it is bounded on its dual space Lp0(·), where 1/p(x) + 1/p0(x) = 1 for x ∈ X. This result extends the corresponding result of Lars Diening from the Euclidean setting of Rn to the setting of spaces (X, d, µ) of homogeneous type.
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spelling Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous typeDyadic cubesHardy–Littlewood maximal operatorSpace of homogeneous typeVariable Lebesgue spaceMathematics(all)We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space Lp(·) over a space of homogeneous type (X, d, µ) if and only if it is bounded on its dual space Lp0(·), where 1/p(x) + 1/p0(x) = 1 for x ∈ X. This result extends the corresponding result of Lars Diening from the Euclidean setting of Rn to the setting of spaces (X, d, µ) of homogeneous type.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovich, Alexei2021-05-05T23:27:40Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article30application/pdfhttp://hdl.handle.net/10362/117157eng0039-3223PURE: 28484164https://doi.org/10.4064/sm180816-16-9info: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:RCAAP2024-03-11T05:00:13Zoai:run.unl.pt:10362/117157Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:43:30.516781Repositório 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 Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
title Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
spellingShingle Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
Karlovich, Alexei
Dyadic cubes
Hardy–Littlewood maximal operator
Space of homogeneous type
Variable Lebesgue space
Mathematics(all)
title_short Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
title_full Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
title_fullStr Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
title_full_unstemmed Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
title_sort Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
author Karlovich, Alexei
author_facet Karlovich, Alexei
author_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Karlovich, Alexei
dc.subject.por.fl_str_mv Dyadic cubes
Hardy–Littlewood maximal operator
Space of homogeneous type
Variable Lebesgue space
Mathematics(all)
topic Dyadic cubes
Hardy–Littlewood maximal operator
Space of homogeneous type
Variable Lebesgue space
Mathematics(all)
description We show that the Hardy–Littlewood maximal operator is bounded on a reflexive variable Lebesgue space Lp(·) over a space of homogeneous type (X, d, µ) if and only if it is bounded on its dual space Lp0(·), where 1/p(x) + 1/p0(x) = 1 for x ∈ X. This result extends the corresponding result of Lars Diening from the Euclidean setting of Rn to the setting of spaces (X, d, µ) of homogeneous type.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2021-05-05T23:27:40Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/117157
url http://hdl.handle.net/10362/117157
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0039-3223
PURE: 28484164
https://doi.org/10.4064/sm180816-16-9
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
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dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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
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