For functions from the sets C ψ β L s , 1 ≤ s ≤ ∞, where ψ(k) > 0 and \( {\lim_{{k\to \infty }}}\frac{{\psi \left( {k+1} \right)}}{{\psi (k)}} \), we obtain asymptotically sharp estimates for the norms of deviations of the de la Vallée-Poussin sums in the uniform metric represented 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 shown that the obtained estimates are sharp on some important functional subsets.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 5, pp. 642–653, May, 2013.
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Musienko, A.P., Serdyuk, A.S. Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions. Ukr Math J 65, 709–722 (2013). https://doi.org/10.1007/s11253-013-0808-4
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DOI: https://doi.org/10.1007/s11253-013-0808-4