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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAMAR, Eric
dc.date.accessioned2024-04-04T02:35:53Z
dc.date.available2024-04-04T02:35:53Z
dc.date.created2009-06-10
dc.date.issued2016
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190681
dc.description.abstractEnLet $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly pseudo-convex points on $\partial \Omega $ is small with respect to Minkowski dimension: near each point in the boundary $\partial \Omega ,$ there is at least one complex tangent direction in which the slices of $W$ has a upper Minkowski dimension strictly smaller than $2.$ We propose to call this notion "strong pseudo-convexity"; this word is free since "strict pseudo-convexity" gets the precedence in the case where all the points in $\partial \Omega $ are stricly pseudo-convex. For such domains we prove that if $S$ is a separated sequence of points contained in the support of a divisor in the Blaschke class, then a canonical measure associated to $S$ is bounded. If moreover the domain is $p$-regular, and the sequence $S$ is dual bounded in the Hardy space $H^{p}(\Omega),$ then the previous measure is Carleson. Examples of such pseudo-convex domains are finite type domains in ${\mathbb{C}}^{2},$ finite type convex domains in ${\mathbb{C}}^{n},$ finite type domains which have locally diagonalizable Levi form, domains with real analytic boundary and of course, stricly pseudo-convex domains in ${\mathbb{C}}^{n}.$ Domains like $|{z_{1}}| ^{2}+\exp \{1-|{z_{2}}| ^{-2}\}<1,$ which are not of finite type are nevertheless strongly pseudo-convex, in this sense.
dc.language.isoen
dc.subject.enInterpolating sequence
dc.subject.enHardy space
dc.subject.enCarleson measures
dc.title.enA weak notion of strict pseudo-convexity. Applications and examples
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv0906.1956
bordeaux.journalAnnali della Scuola Normale Superiore di Pisa
bordeaux.page183-276
bordeaux.volume16
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue5
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00394573
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00394573v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Annali%20della%20Scuola%20Normale%20Superiore%20di%20Pisa&amp;rft.date=2016&amp;rft.volume=16&amp;rft.issue=5&amp;rft.spage=183-276&amp;rft.epage=183-276&amp;rft.au=AMAR,%20Eric&amp;rft.genre=article


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