Abstract
We construct a solution to the partial derivative-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type (0, s), s >= 1, with values in a holomorphic vector bundle which is Nakano positive and for complex valued forms of type (r, s), 1 <= r <= n, when the complex manifold is a Stein manifold. Using Kerzman's techniques, we find the L-p-estimates, 1 <= p <= infinity, for the solution.