Extension and restriction of holomorphic functions
Annales de l'Institut Fourier, Volume 47 (1997) no. 4, p. 1079-1099

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 )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 )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.

@article{AIF_1997__47_4_1079_0,
     author = {Diederich, Klas and Mazzilli, Emmanuel},
     title = {Extension and restriction of holomorphic functions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {4},
     year = {1997},
     pages = {1079-1099},
     doi = {10.5802/aif.1592},
     zbl = {0881.32005},
     mrnumber = {99d:32012},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1997__47_4_1079_0}
}
Diederich, Klas; Mazzilli, Emmanuel. Extension and restriction of holomorphic functions. Annales de l'Institut Fourier, Volume 47 (1997) no. 4, pp. 1079-1099. doi : 10.5802/aif.1592. http://www.numdam.org/item/AIF_1997__47_4_1079_0/

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