Hardy–Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type
Autor(a) principal: | |
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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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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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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 |
format |
article |
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 |
dc.format.none.fl_str_mv |
30 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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1799138044606939136 |