no. 3
Analytic extension from non-pseudoconvex boundaries and A(D)-convexity
[Extension holomorphe depuis un bord non-pseudoconvexe et A(D)-convexité]
Laurent-Thiébaut, Christine1 ; Porten, Egmon2
1 Université Joseph Fourier, Institut Fourier, BP 74, 3802 Saint-Martin d'Hères Cedex (France)
2 Humboldt-University, Mathematics Department, Rudower Chaussee 25, 12489 Berlin (Allemagne)
Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 847-857.

Soit D⊂⊂ℂ n ,n≥2, un domaine à bord C 2 et K⊂∂D un compact tel que ∂D∖K soit connexe. On étudie l’extension holomorphe des fonctions CR définies sur ∂D∖K à des sous-ensembles de D. On dit que K est CR-convexe si son enveloppe A(D)-convexe, A(D)- hull (K), vérifie K=∂D∩A(D)- hull (K) (A(D) désigne l’espace des fonctions holomorphes sur D et continues sur D ¯). Le théorème principal de cet article prouve l’extension holomorphe à ∂D∖A(D)- hull (K), si K est CR-convexe.

Let D⊂⊂ℂ n ,n≥2, be a domain with C 2 -boundary and K⊂∂D be a compact set such that ∂D∖K is connected. We study univalent analytic extension of CR-functions from ∂D∖K to parts of D. Call K CR-convex if its A(D)-convex hull, A(D)- hull (K), satisfies K=∂D∩A(D)- hull (K) (A(D) denoting the space of functions, which are holomorphic on D and continuous up to ∂D). The main theorem of the paper gives analytic extension to ∂D∖A(D)- hull (K), if K is CR- convex.

DOI : 10.5802/aif.1962
Classification : 32V25, 32D10, 32D20
Keywords: holomorphic hulls and holomorphic convexity, CR functions, removable singularities
Mot clés : enveloppes holomorphes et convexité holomorphe, CR fonctions, singularités éliminables

Laurent-Thiébaut, Christine 1 ; Porten, Egmon 2

1 Université Joseph Fourier, Institut Fourier, BP 74, 3802 Saint-Martin d'Hères Cedex (France)
2 Humboldt-University, Mathematics Department, Rudower Chaussee 25, 12489 Berlin (Allemagne) 
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Laurent-Thiébaut, Christine; Porten, Egmon. Analytic extension from non-pseudoconvex boundaries and $A(D)$-convexity. Annales de l'Institut Fourier, Tome 53 (2003) no. 3, pp. 847-857. doi : 10.5802/aif.1962. https://aif.centre-mersenne.org/articles/10.5802/aif.1962/

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