On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness
Classical Analysis and ODEs
2017-04-21 v1
Abstract
In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.
Keywords
Cite
@article{arxiv.1704.06056,
title = {On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness},
author = {Nimete Sh. Berisha and Faton M. Berisha and Mikhail K. Potapov and Marjan Dema},
journal= {arXiv preprint arXiv:1704.06056},
year = {2017}
}
Comments
18 pages. arXiv admin note: substantial text overlap with arXiv:1208.6123