Estimates for some Weighted Bergman Projections
Language
en
Article de revue
This item was published in
Complex Variables and Elliptic Equations. 2014, vol. 59, n° 8, p. 1070-1095
Taylor & Francis
English 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 ...Read more >
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 $\geq n-2$ 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.Read less <
English Keywords
pseudo-convex
finite type
Levi form locally diagonalizable
convex
extremal basis
geometric separation
weighted Bergman projection
$\overline{\partial}_{\varphi}$-Neumann problem}
Origin
Hal imported