Estimates for some Weighted Bergman Projections

Abstract

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in ${\mathbb{C}}^n$. The main result is obtained for weights equal to a non negative rational power of the absolute value of a special defining function $\rho$ of the domain: we prove (weighted) Sobolev-$L^p$ and Lipchitz estimates for domains in ${\mathbb{C}}^2$ (or, more generally, for domains having a Levi form of rank $\ge n-2$ 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-$L^2$ estimate.

Final version. To appear in Complex Variables and Elliptic Equations

References in corpus (1)

• $L^p$ Regularity of Some Weighted Bergman Projections on the Unit Disc