C∞ solvability of the partial derivative system on wedges of CN

We prove existence of C-infinity solutions of the <(partial derivative)over bar> system on open wedges of C-N under a very general condition of weak q-pseudoconvexity, The method relies on the L-2-estimates by Hormander and in our generalization previously introduced in (G. Zampieri, 1998, J. Anal. Math. 74, 99-111). Let us point out that in spire of the only slight improvements in the estimates, much stronger existence theorems are obtained. The <(partial derivative)over bar> problem for wedges of CN is extensively treated in the literature (cf. G. M. Henkin and J. Leiterer, 1988, Andreotti-Grauert Theory by Integral Formulas, Progress in Math., Vol. 74, Birkhauser and the references cited therein). However the usual approach employs integral representations rather than L-2 estimates. (C) 2000 Academic Press.