Approximation by rational functions on doubly connected domains in weighted generalized grand Smirnov classes

Abstract

Let G subset of C be a doubly connected domain bounded by two rectifiable Carleson curves. We use the higher modulus of smoothness in order to investigate the approximation properties of (p - epsilon)-Faber-Laurent rational functions in the subclass of weighted generalized grand Smirnov classes E-p),E-theta (G, omega) of analytic functions.