Sur une extension du problème de Gleason dans les domaines pseudoconvexes

Joaquin M. Ortega

Annales de l'institut Fourier (1984)

  • Volume: 34, Issue: 4, page 67-74
  • ISSN: 0373-0956

Abstract

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In this paper we prove that every f ∈ A ∞ ( D ‾ ) has a decomposition f ( z ) - f ( w ) = ∑ i = 1 n g i ( z , w ) ( z i - w i ) with g i ∈ A ∞ ( D × D ‾ ) , for all pseudoconvex domains with real-analytic boundary, as well as for pseudoconvex domains for which the result holds true locally.

How to cite

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Ortega, Joaquin M.. "Sur une extension du problème de Gleason dans les domaines pseudoconvexes." Annales de l'institut Fourier 34.4 (1984): 67-74. <http://eudml.org/doc/74658>.

@article{Ortega1984,
abstract = {Dans cet article on montre que toute $f\in A^\infty (\overline\{D\})$ a une décomposition $f(z) - f(w) = \sum ^n_\{i=1\} g_i(z,w) (z_i-w_i)$ avec $g_i \in A^\infty (\overline\{D\times D\})$ pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.},
author = {Ortega, Joaquin M.},
journal = {Annales de l'institut Fourier},
keywords = {pseudoconvex domains; Gleason problem; d-bar-equations; real-analytic boundary; closed ideals of holomorphic functions; Kuenneth theorem},
language = {fre},
number = {4},
pages = {67-74},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur une extension du problème de Gleason dans les domaines pseudoconvexes},
url = {http://eudml.org/doc/74658},
volume = {34},
year = {1984},
}

TY - JOUR
AU - Ortega, Joaquin M.
TI - Sur une extension du problème de Gleason dans les domaines pseudoconvexes
JO - Annales de l'institut Fourier
PY - 1984
PB - Association des Annales de l'Institut Fourier
VL - 34
IS - 4
SP - 67
EP - 74
AB - Dans cet article on montre que toute $f\in A^\infty (\overline{D})$ a une décomposition $f(z) - f(w) = \sum ^n_{i=1} g_i(z,w) (z_i-w_i)$ avec $g_i \in A^\infty (\overline{D\times D})$ pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.
LA - fre
KW - pseudoconvex domains; Gleason problem; d-bar-equations; real-analytic boundary; closed ideals of holomorphic functions; Kuenneth theorem
UR - http://eudml.org/doc/74658
ER -

References

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  8. [8] J. J. KOHN, Global regularity for ∂ on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc., 181 (1973), 273-292. Zbl0276.35071MR49 #9442
  9. [9] I. LIEB, Die Cauchy-Riemannschen Differentialgleichung auf streng pseudokonveksen Gebieten : Stetige Randwerte, Math. Ann., 199 (1972), 241-256. Zbl0231.35055MR48 #6468
  10. [10] B. MALGRANGE, Ideals of differentiable functions, Oxford University Press, 1966. Zbl0177.17902
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  13. [13] N. ØVRELID, Generators of the maximal ideals of A(D), Pac. Jour. Math., 39 (1971), 219-233. Zbl0231.46090MR46 #9393

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