Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Dissertação |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10362/135865 |
Resumo: | We prove a version of the Riesz-Thorin interpolation theorem for some types of weighted variable Lebesgue spaces. In order to do this we use the theory developed by Calderón in his 1964 article, together with some Banach function space theory. Using our version of the Riesz-Thorin theorem, we prove a version of the Stechkin inequality forweighted variable Lebesgue spaces, allowing us to define algebras of Fourier multipliers arising from functions of bounded variation. After analyzing the invertibility of Fourier convolution operators with piecewise continuous symbols, we shift our attention to slowly oscillating Fourier multipliers, finishing with a proof that the image in the Calkin algebra of the algebra of convolution type operators with slowly oscillating data is commutative. |
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Algebras of Convolution Type Operators on Weighted Variable Lebesgue SpacesWeighted variable Lebesgue spacesFourier multipliersInterpolationFunctions of bounded variationSlowly oscillating functionsAlgebras of convolution type operatorsDomínio/Área Científica::Ciências Naturais::MatemáticasWe prove a version of the Riesz-Thorin interpolation theorem for some types of weighted variable Lebesgue spaces. In order to do this we use the theory developed by Calderón in his 1964 article, together with some Banach function space theory. Using our version of the Riesz-Thorin theorem, we prove a version of the Stechkin inequality forweighted variable Lebesgue spaces, allowing us to define algebras of Fourier multipliers arising from functions of bounded variation. After analyzing the invertibility of Fourier convolution operators with piecewise continuous symbols, we shift our attention to slowly oscillating Fourier multipliers, finishing with a proof that the image in the Calkin algebra of the algebra of convolution type operators with slowly oscillating data is commutative.Provamos uma versão do teorema de interpolação de Riesz-Thorin para alguns tipos de espaços de Lebesgue com expoente variável e peso. De forma a atingir este objectivo, usamos a teoria desenvolvida por Calderón no seu artigo de 1964. Usando a versão do teorema de Riesz-Thorin obtida, provamos uma versão da desigualdade de Stechkin para espaços de Lebesgue com expoente variável e peso. Isto permite-nos definir álgebras de multiplicadores de Fourier associados a funções de variação limitada. Após analisada a invertibilidade dos operadores de convolução com símbolos contínuos por troços, deslocamos a nossa atenção para multiplicadores de Fourier fracamente oscilantes. Terminamos com a prova de que a imagem na álgebra de Calkin da álgebra de operadores tipo convolução com dados fracamente oscilantes é comutativa.Karlovych, OleksiyFernandes, CláudioRUNMedalha, Samuel João Baltazar2022-04-05T13:46:48Z2021-022021-02-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisapplication/pdfhttp://hdl.handle.net/10362/135865enginfo: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:RCAAP2024-03-11T05:14:10Zoai:run.unl.pt:10362/135865Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:48:32.399050Repositório 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 |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
title |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
spellingShingle |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces Medalha, Samuel João Baltazar Weighted variable Lebesgue spaces Fourier multipliers Interpolation Functions of bounded variation Slowly oscillating functions Algebras of convolution type operators Domínio/Área Científica::Ciências Naturais::Matemáticas |
title_short |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
title_full |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
title_fullStr |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
title_full_unstemmed |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
title_sort |
Algebras of Convolution Type Operators on Weighted Variable Lebesgue Spaces |
author |
Medalha, Samuel João Baltazar |
author_facet |
Medalha, Samuel João Baltazar |
author_role |
author |
dc.contributor.none.fl_str_mv |
Karlovych, Oleksiy Fernandes, Cláudio RUN |
dc.contributor.author.fl_str_mv |
Medalha, Samuel João Baltazar |
dc.subject.por.fl_str_mv |
Weighted variable Lebesgue spaces Fourier multipliers Interpolation Functions of bounded variation Slowly oscillating functions Algebras of convolution type operators Domínio/Área Científica::Ciências Naturais::Matemáticas |
topic |
Weighted variable Lebesgue spaces Fourier multipliers Interpolation Functions of bounded variation Slowly oscillating functions Algebras of convolution type operators Domínio/Área Científica::Ciências Naturais::Matemáticas |
description |
We prove a version of the Riesz-Thorin interpolation theorem for some types of weighted variable Lebesgue spaces. In order to do this we use the theory developed by Calderón in his 1964 article, together with some Banach function space theory. Using our version of the Riesz-Thorin theorem, we prove a version of the Stechkin inequality forweighted variable Lebesgue spaces, allowing us to define algebras of Fourier multipliers arising from functions of bounded variation. After analyzing the invertibility of Fourier convolution operators with piecewise continuous symbols, we shift our attention to slowly oscillating Fourier multipliers, finishing with a proof that the image in the Calkin algebra of the algebra of convolution type operators with slowly oscillating data is commutative. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-02 2021-02-01T00:00:00Z 2022-04-05T13:46:48Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10362/135865 |
url |
http://hdl.handle.net/10362/135865 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
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 |
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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 |
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1799138086856163328 |