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A smoothing property of the Bergman projection

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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 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Vienna, Vienna, Austria

    A.-K. Herbig

  2. Department of Mathematics, Ohio State University, Columbus, OH, USA

    J. D. McNeal

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  1. A.-K. Herbig
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  2. J. D. McNeal
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Correspondence to A.-K. Herbig.

Additional information

Research of the A.-K. Herbig was supported by FWF grants P19147 and AY0037721; Research of the J. D. McNeal was partially supported by an NSF grant.

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Herbig, AK., McNeal, J.D. A smoothing property of the Bergman projection. Math. Ann. 354, 427–449 (2012). https://doi.org/10.1007/s00208-011-0734-4

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  • DOI: https://doi.org/10.1007/s00208-011-0734-4

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