Extension and restriction of holomorphic functions

Diederich, Klas ; Mazzilli, Emmanuel

Annales de l'Institut Fourier, Tome 47 (1997), p. 1079-1099 / Harvested from Numdam

Résumé

De fortes pathologies par rapport aux propriétés de croissance peuvent apparaître pour l’extension des fonctions holomorphes d’une sous-variété $ D^{\prime }$ d’un domaine $ D$ à $ D$ tout entier, même dans des cas très simples; les espaces $ A^{p}(D^{\prime }):={\cal O}(D^{\prime })\cap L^{p}(D^{\prime })$ ne sont, en général, pas tous préservés par extension. De même, la restriction de l’espace de Hilbert $ A^{2}(D)$ à $ D^{\prime }$, peut avoir une structure très étrange.

Abstract

Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds $ D^{\prime }$ of pseudoconvex domains $ D$ to all of $ D$ even in quite simple situations; The spaces $A^{p}(D^{\prime }):={\cal O}(D^{\prime })\cap L^{p}(D^{\prime })$ are, in general, not at all preserved. Also the image of the Hilbert space $ A^{2}(D)$ under the restriction to $ D^{\prime }$ can have a very strange structure.

Détail

Publié le : 1997-01-01

MR 99d:32012 | Zbl 0881.32005

DOI : https://doi.org/10.5802/aif.1592

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