The Bernstein inequalities for trigonometric polynomials are generalized. For sums of Fourier coefficients, upper bounds with certain constants in terms of quantities characterizing structural properties of functions are obtained. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 429, 2014, pp. 64–81.
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Zhuk, V.V., Puerov, G.Y. Some Inequalities for Trigonometric Polynomials and Fourier Coefficients. J Math Sci 207, 845–856 (2015). https://doi.org/10.1007/s10958-015-2409-2
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DOI: https://doi.org/10.1007/s10958-015-2409-2