Carleson measures for Besov spaces on the ball with applications

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dc.citation.epage520en_US
dc.citation.issueNumber2en_US
dc.citation.spage483en_US
dc.citation.volumeNumber250en_US
dc.contributor.authorKaptanoǧlu, Hakkı Turgayen_US
dc.date.accessioned2016-02-08T10:13:01Z
dc.date.available2016-02-08T10:13:01Z
dc.date.issued2007en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractCarleson and vanishing Carleson measures for Besov spaces on the unit ball of CN are characterized in terms of Berezin transforms and Bergman-metric balls. The measures are defined via natural imbeddings of Besov spaces into Lebesgue classes by certain combinations of radial derivatives. Membership in Schatten classes of the imbeddings is considered too. Some Carleson measures are not finite, but the results extend and provide new insight to those known for weighted Bergman spaces. Special cases pertain to Arveson and Dirichlet spaces, and a unified view with the usual Hardy-space Carleson measures is presented by letting the order of the radial derivatives tend to 0. Weak convergence in Besov spaces is also characterized, and weakly 0-convergent families are exhibited. Applications are given to separated sequences, operators of Forelli-Rudin type, gap series, characterizations of weighted Bloch, Lipschitz, and growth spaces, inequalities of Fejér-Riesz and Hardy-Littlewood type, and integration operators of Cesàro type.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:13:01Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2007en
dc.identifier.doi10.1016/j.jfa.2006.12.016en_US
dc.identifier.eissn1096-0783
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/11693/23377
dc.language.isoEnglishen_US
dc.publisherAcademic Pressen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.jfa.2006.12.016en_US
dc.source.titleJournal of Functional Analysisen_US
dc.subjectArvesonen_US
dc.subjectBerezin transformen_US
dc.subjectBergman metricen_US
dc.subjectBergman projectionen_US
dc.subjectBesoven_US
dc.subjectBlochen_US
dc.subjectCarleson measureen_US
dc.subjectCesàro - type operatoren_US
dc.subjectDirichleten_US
dc.subjectFejér - Rieszen_US
dc.subjectForelli - Rudin - type operatoren_US
dc.subjectgrowth spaceen_US
dc.subjectHardyen_US
dc.subjectHardy - Littlewood inequalityen_US
dc.subjectLacunary seriesen_US
dc.subjectLipschitzen_US
dc.subjectSchatten - von Neumann idealen_US
dc.subjectSeparated sequenceen_US
dc.subjectUltraweak convergenceen_US
dc.subjectWeaken_US
dc.subjectBergmanen_US
dc.titleCarleson measures for Besov spaces on the ball with applicationsen_US
dc.typeArticleen_US

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