Boundary regularity for di-bar on q-Pseudoconvex wedges of C^N

For a wedge \u3a9 of CN, we refine the notion of weak q-pseudoconvexity of [G. Zampieri, Solvability of the \uaf 02 problem with C 1e regularity up to the boundary on wedges of CN, Israel J. Math. 115 (2000) 321\u2013331]. This is an intrinsic property which can be expressed in terms of q-subharmonicity both of a defining function or an exhaustion function of \u3a9. Under this condition we prove solvability of the \uaf 02 system for forms with C 1e ( \uaf \u3a9)-coefficients of degree q + 1. Our method relies on the L2-estimates by H\uf6rmander [L. H\uf6rmander, L2 estimates and existence theorems for the \uaf 02 operator, Acta Math. 113 (1965) 89\u2013152] and by Kohn [J.J. Kohn, Global regularity for \uaf 02 on weakly pseudoconvex manifolds, Trans. Amer. Math. Soc. 181 (1973) 273\u2013292]. For solvability with regularity up to the boundary in a domain without corners, we refer to [J.J. Kohn, Methods of partial differential equations in complex analysis, Proc. Sympos. Pure Math. 30 (1977) 215\u2013237] in case of classical pseudoconvexity, that is for q = 0 in our notation (or else for strong pseudoconvexity which means that the number of the positive Levi eigenvalues of the boundary is N 12 1 12 q), and we refer to [L. Baracco, G. Zampieri, Global regularity for \uaf 02 on q-pseudoconvex domains, 2003] for general q-pseudoconvexity. For local existence on wedge-type domains we refer to [G. Zampieri, Solvability of the \uaf 02 problem with C 1e regularity up to the boundary on wedges of CN, Israel J. Math. 115 (2000) 321\u2013331]