Abstract
We obtain Bernstein and Jackson-Nikol’skii inequalities for trigonometric polynomials with spectrum generated by the level surfaces of a function Λ(t), and study their sharpness under a specific choice of Λ(t). Estimates of the norms of derivatives of Dirichlet kernels with harmonics generated by the level surfaces of the function Λ(t) are established in L p .
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Translated from Matematicheskie Zametki, vol. 80, no. 1, 2006, pp. 95–104.
Original Russian Text Copyright © 2006 by M. B. Sikhov.
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Sikhov, M.B. Inequalities of Bernstein and Jackson-Nikol’skii type and estimates of the norms of derivatives of Dirichlet kernels. Math Notes 80, 91–100 (2006). https://doi.org/10.1007/s11006-006-0112-9
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DOI: https://doi.org/10.1007/s11006-006-0112-9