Direct and inverse theorems in variable exponent smirnov classes

Abstract

Let G be a simple connected bounded domain in the complex plane C. Imposing some additional conditions on the variable exponent p (.), we prove direct and inverse theorems of approximation theory in the variable exponent Smirnov classes E-p(.) (G), when the boundary Gamma := partial derivative G is a Carleson curve or so called regular Jordan curve. A constructive characterization of Lipschitz subclass of E-p(.) (G) is also obtained.