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Approximation of polynomials in the Haar system in weighted symmetric spaces

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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.

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Authors and Affiliations

  1. Chernyshevskii Saratov National Research State University, Saratov, Russia

    S. S. Volosivets

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  1. S. S. Volosivets
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Correspondence to S. S. Volosivets.

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Original Russian Text © S. S. Volosivets, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 5, pp. 649–657.

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Volosivets, S.S. Approximation of polynomials in the Haar system in weighted symmetric spaces. Math Notes 99, 643–651 (2016). https://doi.org/10.1134/S0001434616050035

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  • DOI: https://doi.org/10.1134/S0001434616050035

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