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

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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1592/

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