Direct and Inverse Theorems of Approximation Theory in Weighted Variable Exponent Smirnov Classes

Let G be a finite Jordan domain in the complex plane C C , bounded by a Carleson curve Γ Γ and let ω ω be a weight function given on Γ Γ . In this work some direct and inverse theorems of approximation theory in the weighted variable exponent Smirnov classes Eωp(· )(G) E ω p ( · ) ( G ) , under some restrictions on the weight ω ω and variable exponent p(· ) p ( · ) , are proved.