Abstract
Let X be a Stein manifold of complex dimension n >= 2 and be a relatively compact domain with C (2) smooth boundary in X. Assume that Omega is a weakly q-pseudoconvex domain in X. The purpose of this paper is to establish sufficient conditions for the closed range of on Omega. Moreover, we study the -problem on Omega. Specifically, we use the modified weight function method to study the weighted -problem with exact support in Omega. Our method relies on the L (2)-estimates by Hormander (1965) and by Kohn (1973).