2018
Том 70
№ 9

# Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 5, pp 709-722.

Citation Example: Musienko A. P., Serdyuk A. S. Lebesgue-type inequalities for the de la Vallée-poussin sums on sets of entire functions // Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 642–653.

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