Abstract
The purpose of this paper is to construct a solution with LP-estimates, 1 < p less than or equal to infinity, to the equation (partial derivative) over barg = f on strongly q-convex domain of Kahler manifold. This is done for forms of type (n, s), s greater than or equal to max (q, k), with values in a holomorphic vector bundle which is Nakano semi-positive of type k and for forms of type (0, s), q less than or equal to s less than or equal to n - k, with values in a holomorphic vector bundle which is Nakano semi-negative of type k.