Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications

Detalhes bibliográficos
Autor(a) principal: Almeida, Alexandre
Data de Publicação: 2015
Outros Autores: Caetano, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/14981
Resumo: In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spaces. Some other properties, like Sobolev embeddings, are also obtained via atomic representations.
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spelling Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applicationsVariable exponentsBesov–Triebel–Lizorkin spacesAtoms and moleculesSobolev embeddingsIn this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spaces. Some other properties, like Sobolev embeddings, are also obtained via atomic representations.Elsevier2018-07-20T14:00:51Z2015-11-28T00:00:00Z2015-11-282017-11-21T17:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/14981eng0022-123610.1016/j.jfa.2015.11.010Almeida, AlexandreCaetano, Antónioinfo: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:RCAAP2024-02-22T11:27:32Zoai:ria.ua.pt:10773/14981Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:26.265133Repositório 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 Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
title Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
spellingShingle Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
Almeida, Alexandre
Variable exponents
Besov–Triebel–Lizorkin spaces
Atoms and molecules
Sobolev embeddings
title_short Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
title_full Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
title_fullStr Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
title_full_unstemmed Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
title_sort Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications
author Almeida, Alexandre
author_facet Almeida, Alexandre
Caetano, António
author_role author
author2 Caetano, António
author2_role author
dc.contributor.author.fl_str_mv Almeida, Alexandre
Caetano, António
dc.subject.por.fl_str_mv Variable exponents
Besov–Triebel–Lizorkin spaces
Atoms and molecules
Sobolev embeddings
topic Variable exponents
Besov–Triebel–Lizorkin spaces
Atoms and molecules
Sobolev embeddings
description In this article we study atomic and molecular decompositions in 2-microlocal Besov and Triebel–Lizorkin spaces with variable integrability. We show that, in most cases, the convergence implied in such decompositions holds not only in the distributions sense, but also in the function spaces themselves. As an application, we give a simple proof for the denseness of the Schwartz class in such spaces. Some other properties, like Sobolev embeddings, are also obtained via atomic representations.
publishDate 2015
dc.date.none.fl_str_mv 2015-11-28T00:00:00Z
2015-11-28
2017-11-21T17:00:00Z
2018-07-20T14:00:51Z
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/10773/14981
url http://hdl.handle.net/10773/14981
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0022-1236
10.1016/j.jfa.2015.11.010
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.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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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