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Mat. Zametki, 2016, Volume 99, Issue 5, Pages 649–657 (Mi mz10964)  

Approximation of Polynomials in the Haar System in Weighted Symmetric Spaces

S. S. Volosivets

Saratov State University

Abstract: For weighted symmetric (or rearrangement-invariant) spaces with nontrivial Boyd indices and weights from suitable Muckenhoupt classes, the basis property of the Haar system in these spaces and two versions of the direct theorem on the approximation by polynomials in the Haar system are established.

Keywords: approximation by polynomials in the Haar system, weighted symmetric space, basis property of the Haar system, Muckenhoupt class, Hölder's inequality, generalized modulus of continuity, Banach function space.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.1520.2014/K
This work was supported by the Ministry of Education and Science of the Russian Federation (grant no. 1.1520.2014/K).


DOI: https://doi.org/10.4213/mzm10964

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English version:
Mathematical Notes, 2016, 99:5, 643–651

Bibliographic databases:

UDC: 517.518
Received: 06.10.2015
Revised: 12.11.2015

Citation: S. S. Volosivets, “Approximation of Polynomials in the Haar System in Weighted Symmetric Spaces”, Mat. Zametki, 99:5 (2016), 649–657; Math. Notes, 99:5 (2016), 643–651

Citation in format AMSBIB
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