Uniform approximation by [formula omitted]-harmonic functions

Abstract

The Mergelyan and Ahlfors–Beurling estimates for the Cauchy transform give quantitative information on uniform approximation by rational functions with poles off K. We will present an analogous result for an integral transform on the unit sphere in C2 introduced by Henkin, and show how it can be used to study approximation by functions that are locally harmonic with respect to the Kohn Laplacian □b.