A smoothing property of the Bergman projection

Details A smoothing property of the Bergman projection A smoothing property of the Bergman projection

2010-10-26

arxiv.org/abs/1010.5462v1

Mathematics

Complex Variables

23 pages

Scientific paper

Let B be the Bergman projection associated to a domain on which the dbar-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 that are not smooth up to the boundary but are mapped by B to functions which are smooth up to the boundary are explicitly described.

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