Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Abstract

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces A p α where −1 < α < 0 and −1 < α < p − 2. We obtain bounds on how close the approximation is to the true extremal function in the A p α and uniform norms. We also discuss several results on the relation between the Bergman modulus of continuity of a function and how quickly its best polynomial approximants converge to it.