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Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions

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Ukrainian Mathematical Journal Aims and scope

For functions from the sets C β ψ C and C β ψ L s , 1 ≤ s ≤ 1, generated by sequences ψ(k) > 0 satisfying the d’Alembert condition \( {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}}=q,\;q\in \left( {0,1} \right) \), we obtain asymptotically sharp estimates for the deviations of de la Vallée-Poussin sums in the uniform metric in terms of the best approximations of the (ψ, β)-derivatives of functions of this kind by trigonometric polynomials in the metrics of the spaces L s . It is proved that the obtained estimates are sharp in some important functional subsets of C β ψ C and C β ψ L s .

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  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. P. Musienko & A. S. Serdyuk

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  1. A. P. Musienko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 4, pp. 522–537, April, 2013.

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Musienko, A.P., Serdyuk, A.S. Lebesgue-type inequalities for the de la Valée-Poussin sums on sets of analytic functions. Ukr Math J 65, 575–592 (2013). https://doi.org/10.1007/s11253-013-0796-4

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