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Sobolev and Lipschitz estimates for weighted Bergman projections

Published online by Cambridge University Press:  22 January 2016

Der-Chen Chang  and
Bao Qin Li
Der-Chen Chang
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA, drc@math.umd.edu
Bao Qin Li
Affiliation:
Department of Mathematics, Florida International University, University Park, Miami, FL 33199, USAlibaoqin@zeus.fiu.edu
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Abstract

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

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 147 , September 1997 , pp. 147 - 178
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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