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Toeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spaces

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dc.contributor.authorKarlovych, Oleksiy
dc.contributor.institutionCMA - Centro de MatemƔtica e AplicaƧƵes
dc.contributor.institutionDM - Departamento de MatemƔtica
dc.contributor.pblHindawi Publishing Corporation
dc.date.accessioned2018-06-21T22:06:29Z
dc.date.available2018-06-21T22:06:29Z
dc.date.issued2017
dc.descriptionThis 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).
dc.description.abstractLet 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 āˆˆ Lāˆž, 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 āˆˆ Lāˆž (resp., a = 0). Moreover, ||a||L āˆž ā‰¤ ||Ta||ā„¬(H[X]) ā‰¤ ||P||ā„¬(X)||a||L āˆž. 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.en
dc.description.versionpublishersversion
dc.description.versionpublished
dc.format.extent2224186
dc.identifier.doi10.1155/2017/9768210
dc.identifier.issn2314-8896
dc.identifier.otherPURE: 3940496
dc.identifier.otherPURE UUID: c31e0902-4ae4-464b-9721-aaf00be1f672
dc.identifier.otherScopus: 85031903025
dc.identifier.otherWOS: 000412532800001
dc.identifier.urihttp://www.scopus.com/inward/record.url?scp=85031903025&partnerID=8YFLogxK
dc.identifier.urlhttps://www.scopus.com/pages/publications/85031903025
dc.language.isoeng
dc.peerreviewedyes
dc.subjectREARRANGEMENT-INVARIANT SPACES
dc.subjectOSCILLATING WEIGHTS
dc.subjectNORM
dc.subjectAnalysis
dc.titleToeplitz Operators on Abstract Hardy Spaces Built upon Banach Function Spacesen
dc.typejournal article
degois.publication.titleJournal of Function Spaces
degois.publication.volume2017
dspace.entity.typePublication
rcaap.rightsopenAccess

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