On essential norms of singular integral operators with constant coefficients and of the backward shift

Detalhes bibliográficos
Autor(a) principal: Karlovych, Oleksiy
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/10362/150563
Resumo: Received by the editors November 5, 2021. 2020 Mathematics Subject Classification. Primary 45E05, 46E30, 47B38. Key words and phrases. Rearrangement-invariant Banach function space, abstract Hardy singular integral operator, backward shift operator, norm, essential norm, measure of non-compactness. Publisher Copyright: © 2022 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0).
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spelling On essential norms of singular integral operators with constant coefficients and of the backward shiftabstract Hardy singular integral operatorbackward shift operatoressential normmeasure of noncompactnessnormRearrangement-invariant Banach function spaceAlgebra and Number TheoryAnalysisDiscrete Mathematics and CombinatoricsGeometry and TopologyReceived by the editors November 5, 2021. 2020 Mathematics Subject Classification. Primary 45E05, 46E30, 47B38. Key words and phrases. Rearrangement-invariant Banach function space, abstract Hardy singular integral operator, backward shift operator, norm, essential norm, measure of non-compactness. Publisher Copyright: © 2022 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0).Let X be a rearrangement-invariant Banach function space on the unit circle T and let H[X] be the abstract Hardy space built upon X. We prove that if the Cauchy singular integral operator (Formula presented) is τ−t bounded on the space X, then the norm, the essential norm, and the Hausdorff measure of non-compactness of the operator aI + bH with a, b ∈ C, acting on the space X, coincide. We also show that similar equalities hold for the backward shift operator (Formula presented) on the abstract Hardy space H[X]. Our results extend those by Krupnik and Polonskiĭ [Funkcional. Anal. i Priložen. 9 (1975), pp. 73-74] for the operator aI + bH and by the second author [J. Funct. Anal. 280 (2021), p. 11] for the operator S.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovych, OleksiyShargorodsky, Eugene2023-03-14T22:43:39Z2022-03-222022-03-22T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article11application/pdfhttp://hdl.handle.net/10362/150563engPURE: 55643117https://doi.org/10.1090/bproc/118info: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:RCAAP2024-03-11T05:32:35Zoai:run.unl.pt:10362/150563Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:54:11.124471Repositório 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 On essential norms of singular integral operators with constant coefficients and of the backward shift
title On essential norms of singular integral operators with constant coefficients and of the backward shift
spellingShingle On essential norms of singular integral operators with constant coefficients and of the backward shift
Karlovych, Oleksiy
abstract Hardy singular integral operator
backward shift operator
essential norm
measure of noncompactness
norm
Rearrangement-invariant Banach function space
Algebra and Number Theory
Analysis
Discrete Mathematics and Combinatorics
Geometry and Topology
title_short On essential norms of singular integral operators with constant coefficients and of the backward shift
title_full On essential norms of singular integral operators with constant coefficients and of the backward shift
title_fullStr On essential norms of singular integral operators with constant coefficients and of the backward shift
title_full_unstemmed On essential norms of singular integral operators with constant coefficients and of the backward shift
title_sort On essential norms of singular integral operators with constant coefficients and of the backward shift
author Karlovych, Oleksiy
author_facet Karlovych, Oleksiy
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 Karlovych, Oleksiy
Shargorodsky, Eugene
dc.subject.por.fl_str_mv abstract Hardy singular integral operator
backward shift operator
essential norm
measure of noncompactness
norm
Rearrangement-invariant Banach function space
Algebra and Number Theory
Analysis
Discrete Mathematics and Combinatorics
Geometry and Topology
topic abstract Hardy singular integral operator
backward shift operator
essential norm
measure of noncompactness
norm
Rearrangement-invariant Banach function space
Algebra and Number Theory
Analysis
Discrete Mathematics and Combinatorics
Geometry and Topology
description Received by the editors November 5, 2021. 2020 Mathematics Subject Classification. Primary 45E05, 46E30, 47B38. Key words and phrases. Rearrangement-invariant Banach function space, abstract Hardy singular integral operator, backward shift operator, norm, essential norm, measure of non-compactness. Publisher Copyright: © 2022 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0).
publishDate 2022
dc.date.none.fl_str_mv 2022-03-22
2022-03-22T00:00:00Z
2023-03-14T22:43:39Z
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/10362/150563
url http://hdl.handle.net/10362/150563
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv PURE: 55643117
https://doi.org/10.1090/bproc/118
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 11
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
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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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