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Extension of bounded holomorphic functions¶in convex domains

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Abstract:

The E. Amar and G. Henkin theorem on the bounded extendability of bounded holomorphic functions from certain closed complex submanifolds of strictly pseudoconvex domains to the whole domain is generalized to the case of finite type convex domains and their intersections with affine linear hyperplanes. Suitable integral operators of Berndtsson–Andersson type are constructed and estimated for this purpose.

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Authors and Affiliations

  1. Mathematik, Universität Wuppertal, Gausstr. 20, 42095 Wuppertal, Germany e-mail: klas@math.uni-wuppertal.de, , , , , , DE

    Klas Diederich

  2. UFR de Mathématiques Pures et Appliqués, Universitéde Lille 1, 59655 Villeneuve d'Ascq Cedex, France. e-mail: Emmanuel.Mazzilli@agat.univ-lille1.fr, , , , , , FR

    Emmanuel Mazzilli

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  1. Klas Diederich
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  2. Emmanuel Mazzilli
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Received: 7 July 2000

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Diederich, K., Mazzilli, E. Extension of bounded holomorphic functions¶in convex domains. manuscripta math. 105, 1–12 (2001). https://doi.org/10.1007/s002290170007

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  • DOI: https://doi.org/10.1007/s002290170007

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