Multiplier and approximation theorems in Smirnov classes with variable exponent

Let G subset of C be a bounded Jordan domain with a rectifiable Dini-smooth boundary F and let G(-) := ext Gamma. In terms of the higher order modulus of smoothness the direct and inverse problems of approximation theory in the variable exponent Smirnov classes E-p(.) (G) and E-p(.) (G(-)) are investigated. Moreover, the Marcinkiewicz and Littlewood-Paley type theorems are proved. As a corollary some results on the constructive characterization problems in the generalized Lipschitz classes are presented.