Abstract
In this paper we study the Sobolev regularity of the Bergman projection B and the partial derivative-Neumann operator N on a certain pseudo-convex domain. We show that if Omega is a domain with Lipschitz boundary, which is relatively compact in an n-dimensional compact Kahler manifold and satisfies some "log delta-pseudoconvexity" condition, the operators B, N and partial derivative* N are regular in the Sobolev spaces W-r,s(k)(Omega, E) for forms with values in a holomorphic vector bundle E and for any k < eta/2, 0 < eta < 1, 0 <= r <= n, 0 <= s <= n - 1. (C) 2016 Ivane Javakhishvili Tbilisi State University. Published by Elsevier B.V.