The Journal of Geometric Analysis

, Volume 4, Issue 1, pp 91-103

First online:

The Bergman projection as a singular integral operator

  • McNealAffiliated withDepartment of Mathematics, Princeton University

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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 classesL p , 1 <p < ∞.

Math Subject Classification

32H10 32F20 32A40

Key Words and Phrases

Bergman projection pseudometric Calderón-Zygmund operator