A weak notion of strict pseudo-convexity. Applications and examples
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AMAR, Eric | |
| dc.date.accessioned | 2024-04-04T02:35:53Z | |
| dc.date.available | 2024-04-04T02:35:53Z | |
| dc.date.created | 2009-06-10 | |
| dc.date.issued | 2016 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190681 | |
| dc.description.abstractEn | Let $\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.iso | en | |
| dc.subject.en | Interpolating sequence | |
| dc.subject.en | Hardy space | |
| dc.subject.en | Carleson measures | |
| dc.title.en | A weak notion of strict pseudo-convexity. Applications and examples | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 0906.1956 | |
| bordeaux.journal | Annali della Scuola Normale Superiore di Pisa | |
| bordeaux.page | 183-276 | |
| bordeaux.volume | 16 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 5 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00394573 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00394573v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Annali%20della%20Scuola%20Normale%20Superiore%20di%20Pisa&rft.date=2016&rft.volume=16&rft.issue=5&rft.spage=183-276&rft.epage=183-276&rft.au=AMAR,%20Eric&rft.genre=article |
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