Sur une extension du problème de Gleason dans les domaines pseudoconvexes

Ortega, Joaquin M.

Annales de l'Institut Fourier, Tome 34 (1984) no. 4, pp. 67-74.

Dans cet article on montre que toute $f\in A^{\infty }(\overline{D})$ a une décomposition $f\left(z\right)-f\left(w\right)={\sum }_{i=1}^n{g}_i(z,w)(z_i-w_i)$ 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.

In this paper we prove that every $f\in A^{\infty }(\overline{D})$ has a decomposition $f\left(z\right)-f\left(w\right)={\sum }_{i=1}^n{g}_i(z,w)(z_i-w_i)$ with $g_i\in A^{\infty }(\overline{D\times D})$, for all pseudoconvex domains with real-analytic boundary, as well as for pseudoconvex domains for which the result holds true locally.

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