Estimates for weighted Bergman projections on pseudo-convex domains of finite type in ℂn

Abstract

In this paper, we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in . The main result is obtained for weights equal to a non-negative rational power of the absolute value of a special defining function of the domain: we prove (weighted) Sobolev- and Lipschitz estimates for domains in (or, more generally, for domains having a Levi form of rank and for “decoupled” domains) and for convex domains. In particular, for these defining functions, we generalize results obtained by Bonami and Grellier and Chang and Li. We also obtain a general (weighted) Sobolev- estimate.