Finitely generated ideals in A ( ω )

John Erik Fornaess; M. Ovrelid

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 2, page 77-85
  • ISSN: 0373-0956

Abstract

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The Gleason problem is solved on real analytic pseudoconvex domains in C 2 . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a ∂ ‾ question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are R -points as studied by Range and therefore allow local sup-norm estimates for ∂ ‾ .

How to cite

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Fornaess, John Erik, and Ovrelid, M.. "Finitely generated ideals in $A(\omega )$." Annales de l'institut Fourier 33.2 (1983): 77-85. <http://eudml.org/doc/74590>.

@article{Fornaess1983,
abstract = {The Gleason problem is solved on real analytic pseudoconvex domains in $\{\bf C\}^2$. In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a $\bar\{\partial \}$ question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are $R$-points as studied by Range and therefore allow local sup-norm estimates for $\bar\{\partial \}$.},
author = {Fornaess, John Erik, Ovrelid, M.},
journal = {Annales de l'institut Fourier},
keywords = {Gleason problem; real analytic pseudoconvex domains; delta problem; weakly pseudoconvex boundary points; stratification},
language = {eng},
number = {2},
pages = {77-85},
publisher = {Association des Annales de l'Institut Fourier},
title = {Finitely generated ideals in $A(\omega )$},
url = {http://eudml.org/doc/74590},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Fornaess, John Erik
AU - Ovrelid, M.
TI - Finitely generated ideals in $A(\omega )$
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 2
SP - 77
EP - 85
AB - The Gleason problem is solved on real analytic pseudoconvex domains in ${\bf C}^2$. In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a $\bar{\partial }$ question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are $R$-points as studied by Range and therefore allow local sup-norm estimates for $\bar{\partial }$.
LA - eng
KW - Gleason problem; real analytic pseudoconvex domains; delta problem; weakly pseudoconvex boundary points; stratification
UR - http://eudml.org/doc/74590
ER -

References

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  1. [1] F. BEATROUS, Hölder estimates for the Z-equation with a support condition, Pacific J. Math., 90 (1980), 249-257. Zbl0453.32006MR82b:32029
  2. [2] K. DIEDERICH and J. E. FORNÆSS, Pseudoconvex domains : Existence of Stein neighbourhoods, Duke J. Math., 44 (1977), 641-662. Zbl0381.32014
  3. [3] J. E. FORNÆSS and A. NAGEL, The Mergelyan property for weakly pseudoconvex domains, Manuscripta Math., 22 (1977), 199-208. Zbl0391.32010MR56 #15983
  4. [4] A. GLEASON, Finitely generated ideals in Banach algebras, J. Math. Mech., 13 (1964), 125-132. Zbl0117.34105MR28 #2458
  5. [5] G. M. HENKIN, Approximation of functions in pseudoconvex domains and Leibenzon's theorem, Bull. Acad. Pol. Sci. Ser. Math. Astron. et Phys., 19 (1971), 37-42. Zbl0214.33701
  6. [6] N. KERZMAN and A. NAGEL, Finitely generated ideals in certain function algebras, J. Funct. Anal., 7 (1971), 212-215. Zbl0211.43902MR43 #929
  7. [7] J. J. KOHN, Boundary behavior of Z on weakly pseudoconvex manifolds of dimension two, J. Diff. Geom., 6 (1972), 523-542. Zbl0256.35060MR48 #727
  8. [8] J. J. KOHN and L. NIRENBERG, A pseudoconvex domain not admitting a holomorphic support function, Math. Ann., 201 (1973), 265-268. Zbl0248.32013MR48 #8850
  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] S. LOJASIEWICZ, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa, 19 (1965), 449-474. Zbl0128.17101
  11. [11] M. RANGE, Øn Hölder estimates for Zu = f on weakly pseudoconvex domains, Cortona Proceedings, Cortona, 1976-1977, 247-267. Zbl0421.32021
  12. [12] N. ØVRELID, Generators of the maximal ideals of A (D), Pac. J. Math., 39 (1971), 219-233. Zbl0231.46090MR46 #9393

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