A smoothing property of the Bergman projection

Abstract

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.

23 pages