Multiplier and approximation theorems in Smirnov classes with variable exponent

Authors : Daniyal ISRAFILZADE, Ahmet TESTICI

Pages : 1442-1456

View : 10 | Download : 5

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let $G\subset \mathbb{C}$ be a bounded Jordan domain with a rectifiable Dini-smooth boundary $\Gamma $ 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 $E^{pinsert ignore into journalissuearticles values(\cdot );}insert ignore into journalissuearticles values(G);$ and $E^{pinsert ignore into journalissuearticles values(\cdot );}insert ignore into journalissuearticles values(G^{-});$ \ 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.
Keywords : Variable exponent Smirnov classes, direct and inverse theorems, Faber series, Lipschitz classes, Littlewood Paley theorems, Marcinkiewicz theorems