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January 2020 Approximation by trigonometric polynomials in weighted Morrey spaces
Z. Cakir, C. Aykol, D. Soylemez, A. Serbetci
Tbilisi Math. J. 13(1): 123-138 (January 2020). DOI: 10.32513/tbilisi/1585015225

Abstract

In this paper we investigate the best approximation by trigonometric polynomials in weighted Morrey spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$, where the weight function $w$ is in the Muckenhoupt class $A_{p}(I_{0})$ with $1 < p < \infty$ and $I_{0}=[0, 2\pi]$. We prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces $\mathcal{\widetilde{M}}_{p,\lambda}(I_{0},w)$ the closure of $C^{\infty}(I_{0})$ in $\mathcal{M}_{p,\lambda}(I_{0},w)$. We give the characterization of $K-$functionals in terms of the modulus of smoothness and obtain the Bernstein type inequality for trigonometric polynomials in the spaces $\mathcal{M}_{p,\lambda}(I_{0},w)$.

Funding Statement

The research of Z. Cakir and C. Aykol was partially supported by the grant of Ankara University Scientific Research Project (BAP.17B0430003).

Citation

Download Citation

Z. Cakir. C. Aykol. D. Soylemez. A. Serbetci. "Approximation by trigonometric polynomials in weighted Morrey spaces." Tbilisi Math. J. 13 (1) 123 - 138, January 2020. https://doi.org/10.32513/tbilisi/1585015225

Information

Received: 7 September 2019; Accepted: 7 December 2019; Published: January 2020
First available in Project Euclid: 24 March 2020

zbMATH: 1427.42001
MathSciNet: MR4079455
Digital Object Identifier: 10.32513/tbilisi/1585015225

Subjects:
Primary: 41A10
Secondary: 41A25, 42A10, 46E30, 46E35

Rights: Copyright © 2020 Tbilisi Centre for Mathematical Sciences

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Vol.13 • No. 1 • January 2020
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