Uniform Approximation of Extremal Functions in Weighted Bergman Spaces

Abstract

We discuss approximation of extremal functions by polynomials in the weighted Bergman spaces $A_{\alpha }^p$ where $-1<\alpha <0$ and $-1<\alpha <p-2$. We obtain bounds on how close the approximation is to the true extremal function in the $A_{\alpha }^p$ 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.

11 pages