Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces

Detalhes bibliográficos
Autor(a) principal: Karlovych, Oleksiy
Data de Publicação: 2017
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://doi.org/10.1155/2017/9768210
Resumo: This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).
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spelling Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function SpacesREARRANGEMENT-INVARIANT SPACESOSCILLATING WEIGHTSNORMAnalysisThis work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).Let X be a Banach function space over the unit circle T and let H[X] be the abstract Hardy space built upon X. If the Riesz projection P is bounded on X and a ∈ L∞, then the Toeplitz operator Taf = P(af) is bounded on H[X]. We extend well-known results by Brown and Halmos for X = L2 and show that, under certain assumptions on the space X, the Toeplitz operator Ta is bounded (resp., compact) if and only if a ∈ L∞ (resp., a = 0). Moreover, ||a||L ∞ ≤ ||Ta||ℬ(H[X]) ≤ ||P||ℬ(X)||a||L ∞. These results are specified to the cases of abstract Hardy spaces built upon Lebesgue spaces with Muckenhoupt weights and Nakano spaces with radial oscillating weights.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovych, Oleksiy2018-06-21T22:06:29Z20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://doi.org/10.1155/2017/9768210eng2314-8896PURE: 3940496http://www.scopus.com/inward/record.url?scp=85031903025&partnerID=8YFLogxKhttps://doi.org/10.1155/2017/9768210info: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:RCAAP2024-03-11T04:21:54Zoai:run.unl.pt:10362/39935Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:31:12.208350Repositório 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 Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
title Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
spellingShingle Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
Karlovych, Oleksiy
REARRANGEMENT-INVARIANT SPACES
OSCILLATING WEIGHTS
NORM
Analysis
title_short Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
title_full Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
title_fullStr Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
title_full_unstemmed Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
title_sort Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces
author Karlovych, Oleksiy
author_facet Karlovych, Oleksiy
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 Karlovych, Oleksiy
dc.subject.por.fl_str_mv REARRANGEMENT-INVARIANT SPACES
OSCILLATING WEIGHTS
NORM
Analysis
topic REARRANGEMENT-INVARIANT SPACES
OSCILLATING WEIGHTS
NORM
Analysis
description This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matematica e Aplicacoes).
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01T00:00:00Z
2018-06-21T22:06:29Z
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 https://doi.org/10.1155/2017/9768210
url https://doi.org/10.1155/2017/9768210
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 2314-8896
PURE: 3940496
http://www.scopus.com/inward/record.url?scp=85031903025&partnerID=8YFLogxK
https://doi.org/10.1155/2017/9768210
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
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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