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On the interpolation constants for variable Lebesgue spaces

2023-07Artigo 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.pblJohn Wiley & Sons, Ltd.
dc.date.accessioned2023-07-17T22:16:23Z
dc.date.available2024-08-02T00:32:18Z
dc.date.embargoedUntil2024-08-01
dc.date.issued2023-07
dc.descriptionPublisher Copyright: © 2023 Wiley-VCH GmbH.
dc.description.abstractFor (Formula presented.) and variable exponents (Formula presented.) and (Formula presented.) with values in [1, ∞], let the variable exponents (Formula presented.) be defined by (Formula presented.) The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space (Formula presented.) to the variable Lebesgue space (Formula presented.) for (Formula presented.), then (Formula presented.) where C is an interpolation constant independent of T. We consider two different modulars (Formula presented.) and (Formula presented.) generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that (Formula presented.) and (Formula presented.), as well as, lead to sufficient conditions for (Formula presented.) and (Formula presented.). We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that (Formula presented.), (Formula presented.) are Lipschitz continuous and bounded away from one and infinity (in this case, (Formula presented.)).en
dc.description.versionauthorsversion
dc.description.versionpublished
dc.format.extent26
dc.format.extent427401
dc.identifier.doi10.1002/mana.202100549
dc.identifier.issn0025-584X
dc.identifier.otherPURE: 66128709
dc.identifier.otherPURE UUID: 3fff1843-3df8-4f59-9f37-4857887e94c7
dc.identifier.otherScopus: 85152251816
dc.identifier.otherWOS: 000974370000001
dc.identifier.urihttp://hdl.handle.net/10362/155423
dc.identifier.urlhttps://www.scopus.com/pages/publications/85152251816
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.subjectCalderón product
dc.subjectcomplex method of interpolation
dc.subjectinterpolation constant
dc.subjectRiesz–Thorin interpolation theorem
dc.subjectvariable Lebesgue space
dc.subjectGeneral Mathematics
dc.titleOn the interpolation constants for variable Lebesgue spacesen
dc.typejournal article
degois.publication.firstPage2877
degois.publication.issue7
degois.publication.lastPage2902
degois.publication.titleMathematische Nachrichten
degois.publication.volume296
dspace.entity.typePublication
oaire.awardNumberUIDB/00297/2020
oaire.awardTitleCenter for Mathematics and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT
oaire.fundingStream6817 - DCRRNI ID
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsopenAccess
relation.isProjectOfPublicationd00ae22f-ec2b-47b2-935e-60cb44493cc6
relation.isProjectOfPublication.latestForDiscoveryd00ae22f-ec2b-47b2-935e-60cb44493cc6

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