, Volume 354, Issue 2, pp 427-449

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.

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.