Solvability of the (partial derivative)over-bar problem with C∞ regularity up to the boundary on wedges of CN

For a wedge W of C-N, we introduce an intrinsic condition of weak q-pseudoconvexity which can be expressed in terms of q-subharmonicity both of a defining function or an exhaustion function. Under this condition we prove solvability of the partial derivative system for forms with C-infinity((W) over bar)-coefficients of degree greater than or equal to q + 1. Our method relies on the L-2-estimates by Hormander. For C-infinity(W) solvability we refer to Hormander (if partial derivative W is an element of C-2), and to Zampieri (for general wedges W). For C infinity((W) over bar) solvability and with partial derivative W is an element of C-2, we refer to Dufresnoy (if q = 0), Michel (if the number of negative Levi-eigenvalues of partial derivative W is constant), and finally Zampieri (for more general q-pseudoconvexity).