Extension and restriction of holomorphic functions

Diederich, Klas; Mazzilli, Emmanuel

doi:10.5802/aif.1592

Diederich, Klas ; Mazzilli, Emmanuel

Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1079-1099

Abstract (VO)
Résumé

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

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

MR Zbl

DOI : 10.5802/aif.1592

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     author = {Diederich, Klas and Mazzilli, Emmanuel},
     title = {Extension and restriction of holomorphic functions},
     journal = {Annales de l'Institut Fourier},
     pages = {1079--1099},
     year = {1997},
     publisher = {Association des Annales de l'Institut Fourier},
     volume = {47},
     number = {4},
     doi = {10.5802/aif.1592},
     mrnumber = {99d:32012},
     zbl = {0881.32005},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1592/}
}

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Diederich, Klas; Mazzilli, Emmanuel. Extension and restriction of holomorphic functions. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1079-1099. doi: 10.5802/aif.1592

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