Extension and restriction of holomorphic functions

Klas Diederich; Emmanuel Mazzilli

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1079-1099
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Diederich, Klas, and Mazzilli, Emmanuel. "Extension and restriction of holomorphic functions." Annales de l'institut Fourier 47.4 (1997): 1079-1099. <http://eudml.org/doc/75255>.

@article{Diederich1997,
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.},
author = {Diederich, Klas, Mazzilli, Emmanuel},
journal = {Annales de l'institut Fourier},
keywords = {extension of holomorphic functions; -spaces; weighted Bergman spaces; pseudoellipsoids},
language = {eng},
number = {4},
pages = {1079-1099},
publisher = {Association des Annales de l'Institut Fourier},
title = {Extension and restriction of holomorphic functions},
url = {http://eudml.org/doc/75255},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Diederich, Klas
AU - Mazzilli, Emmanuel
TI - Extension and restriction of holomorphic functions
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1079
EP - 1099
AB - 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.
LA - eng
KW - extension of holomorphic functions; -spaces; weighted Bergman spaces; pseudoellipsoids
UR - http://eudml.org/doc/75255
ER -

References

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