The Bergman projection as a singular integral operator Article Received: 02 February 1993 DOI:
Cite this article as: McNeal J Geom Anal (1994) 4: 91. doi:10.1007/BF02921594 Abstract
We show that the Bergman projection operator, associated to one of three classes of domains (all smoothly bounded)-a finite type domain ℂ
2; a decoupled, finite type domain in ℂ n; or a convex, finite type domain in wf n-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 classes L , 1 < p p < ∞. Math Subject Classification 32H10 32F20 32A40 Key Words and Phrases Bergman projection pseudometric Calderón-Zygmund operator
Research partially supported by an NSF postdoctoral fellowship.
Communicated by Reese Harvey
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