Finitely generated ideals in A(ω)
Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 77-85.

Le problème de Gleason est résolu dans le cas particulier des domaines analytiques réels pseudo-convexes de C2. Dans ce cas, les points faiblement pseudo-convexes peuvent former un sous-ensemble de dimension 2 du bord.

Le problème de Gleason est ramené à une question sur ∂¯ en montrant que l’ensemble des points de Kohn-Nirenberg a au plus une dimension. En fait, exception faite d’un sous-ensemble unidimensionnel, les points faiblement pseudo-convexes du bord sont des R-points comme ceux étudiés par Range et admettent donc des estimations de ∂¯ par des normes de la borne supérieure locales.

The Gleason problem is solved on real analytic pseudoconvex domains in C2. 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 ∂¯.

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     author = {Fornaess, John Erik and Ovrelid, M.},
     title = {Finitely generated ideals in $A(\omega )$},
     journal = {Annales de l'Institut Fourier},
     pages = {77--85},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {33},
     number = {2},
     year = {1983},
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Fornaess, John Erik; Ovrelid, M. Finitely generated ideals in $A(\omega )$. Annales de l'Institut Fourier, Tome 33 (1983) no. 2, pp. 77-85. doi : 10.5802/aif.916. https://www.numdam.org/articles/10.5802/aif.916/

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