Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity

[Extension holomorphe depuis un bord non-pseudoconvexe et $A(D)$-convexité]

Laurent-Thiébaut, Christine ; Porten, Egmon

Annales de l'Institut Fourier, Tome 53 (2003), p. 847-857 / Harvested from Numdam

Résumé

Soit $D\subset \subset {\mathbb {C}}^n,n\ge 2$, un domaine à bord $C^2$ et $K\subset \partial D$ un compact tel que $\partial D\backslash K$ soit connexe. On étudie l’extension holomorphe des fonctions CR définies sur $\partial D\backslash K$ à des sous-ensembles de $D$. On dit que $K$ est CR-convexe si son enveloppe $A(D)$-convexe, $A(D)-{\rm hull}(K)$, vérifie $K=\partial D\cap A(D)-{\rm hull}(K)$ ($A(D)$ désigne l’espace des fonctions holomorphes sur $D$ et continues sur $\overline{D}$). Le théorème principal de cet article prouve l’extension holomorphe à $\partial D\backslash A(D)-{\rm hull}(K)$, si $K$ est CR-convexe.

Abstract

Let $D\subset \subset {\mathbb {C}}^n,n\ge 2$, be a domain with $C^2$-boundary and $K\subset \partial D$ be a compact set such that $\partial D\backslash K$ is connected. We study univalent analytic extension of CR-functions from $\partial D\backslash K$ to parts of $D$. Call $K$ CR-convex if its $A(D)$-convex hull, $A(D)-{\rm hull}(K)$, satisfies $K=\partial D\cap A(D)-{\rm hull}(K)$ ($A(D)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$). The main theorem of the paper gives analytic extension to $\partial D\backslash A(D)-{\rm hull}(K)$, if $K$ is CR- convex.

Détail

Publié le : 2003-01-01

MR 2008443 | Zbl 1035.32020

DOI : https://doi.org/10.5802/aif.1962
Classification:  32V25,  32D10,  32D20
Mots clés: enveloppes holomorphes et convexité holomorphe, CR fonctions, singularités éliminables

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