A lower estimate for weak-type Fourier multipliers

Detalhes bibliográficos
Autor(a) principal: Karlovich, Alexei
Data de Publicação: 2022
Outros Autores: Shargorodsky, Eugene
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/134767
Resumo: UIDB/00297/2020
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spelling A lower estimate for weak-type Fourier multipliers42B1546E30abstract Lorentz spaceBanach function spacecontinuous embeddingFourier multiplierweak doubling propertyAnalysisNumerical AnalysisComputational MathematicsApplied MathematicsUIDB/00297/2020Asmar et al. [Note on norm convergence in the space of weak type multipliers. J Operator Theory. 1998;39(1):139–149] proved that the space of weak-type Fourier multipliers acting from (Formula presented.) into (Formula presented.) is continuously embedded into (Formula presented.). We obtain a sharper result in the setting of abstract Lorentz spaces (Formula presented.) with (Formula presented.) built upon a Banach function space X on (Formula presented.). We consider a source space (Formula presented.) and a target space (Formula presented.) in the class of admissible spaces (Formula presented.). Let (Formula presented.) denote the space of Fourier multipliers acting from (Formula presented.) to (Formula presented.). We show that if the space X satisfies the weak doubling property, then the space (Formula presented.) is continuously embedded into (Formula presented.) for every (Formula presented.). This implies that (Formula presented.) is a quasi-Banach space for all choices of source and target spaces (Formula presented.).CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovich, AlexeiShargorodsky, Eugene2022-03-17T23:23:19Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article19application/pdfhttp://hdl.handle.net/10362/134767eng1747-6933PURE: 42333017https://doi.org/10.1080/17476933.2021.1958796info: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:RCAAP2024-03-11T05:13:14Zoai:run.unl.pt:10362/134767Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:48:13.844400Repositório 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 A lower estimate for weak-type Fourier multipliers
title A lower estimate for weak-type Fourier multipliers
spellingShingle A lower estimate for weak-type Fourier multipliers
Karlovich, Alexei
42B15
46E30
abstract Lorentz space
Banach function space
continuous embedding
Fourier multiplier
weak doubling property
Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics
title_short A lower estimate for weak-type Fourier multipliers
title_full A lower estimate for weak-type Fourier multipliers
title_fullStr A lower estimate for weak-type Fourier multipliers
title_full_unstemmed A lower estimate for weak-type Fourier multipliers
title_sort A lower estimate for weak-type Fourier multipliers
author Karlovich, Alexei
author_facet Karlovich, Alexei
Shargorodsky, Eugene
author_role author
author2 Shargorodsky, Eugene
author2_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
Shargorodsky, Eugene
dc.subject.por.fl_str_mv 42B15
46E30
abstract Lorentz space
Banach function space
continuous embedding
Fourier multiplier
weak doubling property
Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics
topic 42B15
46E30
abstract Lorentz space
Banach function space
continuous embedding
Fourier multiplier
weak doubling property
Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics
description UIDB/00297/2020
publishDate 2022
dc.date.none.fl_str_mv 2022-03-17T23:23:19Z
2022
2022-01-01T00:00:00Z
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/10362/134767
url http://hdl.handle.net/10362/134767
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1747-6933
PURE: 42333017
https://doi.org/10.1080/17476933.2021.1958796
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 19
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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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
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