Turkish Journal of Mathematics
DOI
10.3906/mat-1707-15
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.
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, DANIYAL and TESTICI, AHMET
(2018)
"Multiplier and approximation theorems in Smirnov classes withvariable exponent,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 55.
https://doi.org/10.3906/mat-1707-15
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/55
