Estimates for Weighted Bergman Projections on Pseudo-convex Domains of Finite Type in C
نویسندگان
چکیده
In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in C. The main result is obtained for weights equal to a non-negative rational power of the absolute value of a special defining function ρ of the domain: we prove (weighted) Sobolev-L and Lipschitz estimates for domains in C2 (or, more generally, for domains having a Levi form of rank ≥ n− 2 and for “decoupled” domains) and for convex domains. In particular, for these defining functions, we generalize results obtained by A. Bonami & S. Grellier and D. C. Chang & B. Q. Li. We also obtain a general (weighted) Sobolev-L2 estimate.
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