Sobolev estimates for the complex green operator on a class of weakly pseudoconvex boundaries

Abstract

On the boundary of a smooth bounded convex domain in Cn (more generally, a domain that admits a defining funtion that is plurisubharmonic on the boundary), the canonicl (narm-minimizing) solution operator of the -equation, the inverse of □b (the complex Gereen Operator) and the Szegö projection are continuous is Sobolev norms.