Mathematische Annalen

, Volume 354, Issue 2, pp 427–449

A smoothing property of the Bergman projection


    • Department of MathematicsUniversity of Vienna
  • J. D. McNeal
    • Department of MathematicsOhio State University

DOI: 10.1007/s00208-011-0734-4

Cite this article as:
Herbig, A. & McNeal, J.D. Math. Ann. (2012) 354: 427. doi:10.1007/s00208-011-0734-4


Let B be the Bergman projection associated to a domain Ω on which the \({\bar\partial}\) -Neumann operator is compact. We show that arbitrary L 2 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