SOBOLEV AND LIPSCHITZ ESTIMATES FOR WEIGHTED BERGMAN PROJECTIONS

Let Omega be a bounded, decoupled pseudo-convex domain of finite type in C-n with smooth boundary. In this paper, we generalize results of B onami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to t he boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipsc hitz estimates; both of isotropic and anisotropic type, for these proj ections.