Boundary Regularity of Conformal Maps

Abstract

It is a truism that the Riemann mapping theorem allows us to transfer the complex function theory of any simply connected domain (except the plane itself) back to the unit disk, or vice versa. But many of the more delicate questions require something more. If we wish to study behavior of functions at the boundary, or growth or regularity conditions, then we must know something about the boundary behavior of the conformal mapping.