Turkish Journal of Mathematics
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 $E^{p(\cdot )}(G)$ and $E^{p(\cdot )}(G^{-})$ \ 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.
DOI
10.3906/mat-1707-15
Keywords
Variable exponent Smirnov classes, direct and inverse theorems, Faber series, Lipschitz classes, Littlewood-Paley theorems, Marcinkiewicz theorems
First Page
1442
Last Page
1456
Recommended Citation
ISRAFILZADE, D, & TESTICI, A (2018). Multiplier and approximation theorems in Smirnov classes withvariable exponent. Turkish Journal of Mathematics 42 (3): 1442-1456. https://doi.org/10.3906/mat-1707-15
