Abstract
Let D be a weakly q-convex domain in the complex projective space CPn. In this paper, the (weighted) partial derivative-Cauchy problem with support conditions in D is studied. Specifically, the modified weight function method is used to study the L-2 existence theorem for the partial derivative-Neumann problem on D. The solutions are used to study function theory on weakly q-convex domains via the partial derivative-Cauchy problem.