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Bounded compact and dual compact approximation properties of Hardy spaces

2024-01Artigo científico Acesso aberto
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dc.contributor.authorKarlovych, Oleksiy
dc.contributor.authorShargorodsky, Eugene
dc.contributor.institutionCMA - Centro de Matemática e Aplicações
dc.contributor.institutionDM - Departamento de Matemática
dc.contributor.pblElsevier BV
dc.date.accessioned2024-09-24T22:21:19Z
dc.date.available2024-09-24T22:21:19Z
dc.date.issued2024-01
dc.descriptionPublisher Copyright: © 2023 The Author(s)
dc.description.abstractThe aim of the paper is to highlight some open problems concerning approximation properties of Hardy spaces. We also present some results on the bounded compact and the dual compact approximation properties (shortly, BCAP and DCAP) of such spaces, to provide background for the open problems. Namely, we consider abstract Hardy spaces H[X(w)] built upon translation-invariant Banach function spaces X with weights w such that w∈X and w−1∈X′, where X′ is the associate space of X. We prove that if X is separable, then H[X(w)] has the BCAP with the approximation constant M(H[X(w)])≤2. Moreover, if X is reflexive, then H[X(w)] has the BCAP and the DCAP with the approximation constants M(H[X(w)])≤2 and M∗(H[X(w)])≤2, respectively. In the case of classical weighted Hardy space Hp(w)=H[Lp(w)] with 1<p<∞, one has a sharper result: M(Hp(w))≤2|1−2/p| and M∗(Hp(w))≤2|1−2/p|.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent16
dc.format.extent336797
dc.identifier.doi10.1016/j.indag.2023.10.004
dc.identifier.issn0019-3577
dc.identifier.otherPURE: 93322698
dc.identifier.otherPURE UUID: 3e45327d-0f31-4e4e-a173-2527862fc40d
dc.identifier.otherScopus: 85175318139
dc.identifier.otherWOS: 001158799000001
dc.identifier.urihttp://hdl.handle.net/10362/172330
dc.identifier.urlhttps://www.scopus.com/pages/publications/85175318139
dc.language.isoeng
dc.peerreviewedyes
dc.relationinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
dc.relationCenter for Mathematics and Applications
dc.relationCenter for Mathematics and Applications
dc.subjectBounded compact and dual compact approximation properties
dc.subjectTranslation-invariant Banach function space
dc.subjectWeighted Hardy space
dc.subjectGeneral Mathematics
dc.titleBounded compact and dual compact approximation properties of Hardy spacesen
dc.title.subtitleNew results and open problemsen
dc.typejournal article
degois.publication.firstPage143
degois.publication.issue1
degois.publication.lastPage158
degois.publication.titleIndagationes Mathematicae
degois.publication.volume35
dspace.entity.typePublication
oaire.awardNumberUIDB/00297/2020
oaire.awardNumberUIDP/00297/2020
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F00297%2F2020/PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublicationd00ae22f-ec2b-47b2-935e-60cb44493cc6
relation.isProjectOfPublication65d392f7-8781-4d70-b9f3-069b07d4a311
relation.isProjectOfPublication.latestForDiscovery65d392f7-8781-4d70-b9f3-069b07d4a311

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