Estimates for some Weighted Bergman Projections

2012/12/05 by Charpentier, Philippe, Dupain, Yves, Mounkaila, Modi
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.1078

Abstract

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in ℂⁿ. 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^p and Lipchitz 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.

Related

• On estimates for weighted Bergman projections
• Weighted estimates of the Bergman projection with matrix weights
• Weighted estimates for solutions of the ∂ -equation for lineally convex domains of finite type and applications to weighted bergman projections
• On Weighted L^p-Sobolev Estimates for Solutions of the ∂-equation on Lineally Convex Domains of Finite Type and Application
• The Bergman projection in L^p for domains with minimal smoothness