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On the magnitude of Vilenkin–Fourier coefficients

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Abstract

Estimates for the magnitude of Vilenkin–Fourier coefficients of functions from generalized Hölder spaces, some p-fluctuation spaces, and bounded \(\Lambda \)-\(\varphi \)-fluctuation spaces are provided. For the Hölder spaces, p-fluctuation spaces, and spaces of functions of bounded \(\Lambda \)-p-fluctuation we show sharpness of these estimates. Also we prove a Siddiqi-type result on density of indexes n such that \(|{\hat{f}}(n)|\) has the least order of decreasing.

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Authors and Affiliations

  1. Saratov State University, 83 Astrakhanskya str., Saratov, 410012, Russia

    Sergey S. Volosivets & Maria A. Kuznetsova

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  1. Sergey S. Volosivets
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  2. Maria A. Kuznetsova
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Correspondence to Sergey S. Volosivets.

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The first author was supported by the Ministry of Science and Education of the Russian Federation in the framework of the basic part of the scientific research state task, project FSRR-2020-0006. The second author was supported by Grant No. 19-71-00009 of the Russian Science Foundation.

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Volosivets, S.S., Kuznetsova, M.A. On the magnitude of Vilenkin–Fourier coefficients. European Journal of Mathematics 7, 374–389 (2021). https://doi.org/10.1007/s40879-020-00437-6

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  • DOI: https://doi.org/10.1007/s40879-020-00437-6

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