The Journal of Geometric Analysis

, Volume 4, Issue 1, pp 91–103

The Bergman projection as a singular integral operator

Article

DOI: 10.1007/BF02921594

Cite this article as:
McNeal J Geom Anal (1994) 4: 91. doi:10.1007/BF02921594
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Abstract

We show that the Bergman projection operator, associated to one of three classes of domains (all smoothly bounded)-a finite type domain ℂ2; a decoupled, finite type domain in ℂn; or a convex, finite type domain in wfn-may be viewed as a generalized Calderón-Zygmund operator. As an application of this observation, we show that the Bergman projector on any of these domains preserves the Lebesgue classesLp, 1 <p < ∞.

Math Subject Classification

32H10 32F20 32A40 

Key Words and Phrases

Bergman projection pseudometric Calderón-Zygmund operator 

Copyright information

© Mathematica Josephina, Inc. 1994

Authors and Affiliations

  • McNeal
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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