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One-box conditions for Carleson measures for the Dirichlet space

hal.structure.identifierDépartement de Mathématiques
dc.contributor.authorEL-FALLAH, Omar
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorKELLAY, Karim
hal.structure.identifierDépartement de Mathématiques et de Statistiques
dc.contributor.authorMASHREGHI, Javad
hal.structure.identifierDépartement de Mathématiques et de Statistiques
dc.contributor.authorRANSFORD, Thomas
dc.date.accessioned2024-04-04T02:21:56Z
dc.date.available2024-04-04T02:21:56Z
dc.date.issued2015-02-01
dc.identifier.issn0002-9939
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189613
dc.description.abstractEnWe give a simple proof of the fact that a finite measure $\mu$ on the unit disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson one-box condition $\mu(S(I))=O(\phi(|I|))$, where $\phi: (0, 2 ] \to (0,1)$ is an increasing function such that \[ \int_{0}^{2\pi}(\phi (x)/x) dx < \infty/ \] We further show that the integral condition on $\phi$ is sharp.
dc.language.isoen
dc.publisherAmerican Mathematical Society
dc.title.enOne-box conditions for Carleson measures for the Dirichlet space
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
bordeaux.journalProceedings of the American Mathematical Society
bordeaux.page679-684
bordeaux.volume143
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue2
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00835052
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00835052v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&amp;rft.date=2015-02-01&amp;rft.volume=143&amp;rft.issue=2&amp;rft.spage=679-684&amp;rft.epage=679-684&amp;rft.eissn=0002-9939&amp;rft.issn=0002-9939&amp;rft.au=EL-FALLAH,%20Omar&amp;KELLAY,%20Karim&amp;MASHREGHI,%20Javad&amp;RANSFORD,%20Thomas&amp;rft.genre=article


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