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 classesL p, 1 <p < ∞.
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Communicated by Reese Harvey
Research partially supported by an NSF postdoctoral fellowship.
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McNeal The Bergman projection as a singular integral operator. J Geom Anal 4, 91–103 (1994). https://doi.org/10.1007/BF02921594
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DOI: https://doi.org/10.1007/BF02921594