C∞ Solvability of the ∂̄ System on Wedges of CN

AbstractWe prove existence of C∞ solutions of the ∂̄ system on open wedges of CN under a very general condition of weak q-pseudoconvexity. The method relies on the L2-estimates by Hörmander and in our generalization previously introduced in (G. Zampieri, 1998, J. Anal. Math.74, 99–111). Let us point out that in spite of the only slight improvements in the estimates, much stronger existence theorems are obtained. The ∂̄ 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, Birkhäuser and the references cited therein). However the usual approach employs integral representations rather than L2 estimates