We establish two-sided estimates for deviations of Riesz sums on the class of even functions with nonnegative Fourier coefficients. Estimates are obtained by using the fractional modulus of continuity of the function itself and the fractional Hilbert transform of its derivative in the sense of Weyl. The constants are expressed in an explicit form.
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Translated from Problemy Matematicheskogo Analiza101, 2019, pp. 35-55.
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Babushkin, M.V. Approximation of Even Functions with Nonnegative Fourier Coefficients by Fractional Riesz Sums. J Math Sci 244, 576–600 (2020). https://doi.org/10.1007/s10958-019-04634-x
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DOI: https://doi.org/10.1007/s10958-019-04634-x