Journal of Function Spaces

Journal of Function Spaces / 2010 / Article

Open Access

Volume 8 |Article ID 372106 | https://doi.org/10.1155/2010/372106

Vakhtang Kokilashvili, Yunus E. Yildirir, "On the approximation by trigonometric polynomials in weighted Lorentz spaces", Journal of Function Spaces, vol. 8, Article ID 372106, 20 pages, 2010. https://doi.org/10.1155/2010/372106

On the approximation by trigonometric polynomials in weighted Lorentz spaces

Academic Editor: Henrik Hudzik
Received01 Oct 2008

Abstract

We obtain estimates of structural characteristics of 2π-periodic functions by the best trigonometric approximations in weighted Lorentz spaces, and show that the order of generalized modulus of smoothness depends not only on the rate of the best approximation, but also on the metric of the spaces. In weighted Lorentz spaces Lps, this influence is expressed not only in terms of the parameter p, but also in terms of the second parameter s.

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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