Mathematische Annalen

, Volume 354, Issue 2, pp 427–449

A smoothing property of the Bergman projection

Article

Abstract

Let B be the Bergman projection associated to a domain Ω on which the \({\bar\partial}\) -Neumann operator is compact. We show that arbitrary L2 derivatives of Bf are controlled by derivatives of f taken in a single, distinguished direction. As a consequence, functions not contained in \({C^{\infty}(\overline{\Omega})}\) that are mapped by B to \({C^{\infty}(\overline{\Omega})}\) are explicitly described.

Mathematics Subject Classification (2000)

32A25 32W05 

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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ViennaViennaAustria
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

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