Local Boundary Regularity of the Szego Projection and Biholomorphic Mappings of Non-Pseudoconvex Domains

Abstract

It is shown that the Szegő projection S S of a smoothly bounded domain Ω \Omega , not necessarily pseudoconvex, satisfies local regularity estimates at certain boundary points, provided that condition R R holds for Ω \Omega . It is also shown that any biholomorphic mapping f : Ω → D f:\Omega \rightarrow D between smoothly bounded domains extends smoothly near such points, provided that a weak regularity assumption holds for D D .