2017
Том 69
№ 9

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Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics

Serdyuk A. S.

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Abstract

On the classes of Poisson integrals of functions belonging to the unit balls of the spaces $L_s , 1 ≤ s ≤ ∞$, we establish asymptotic equalities for upper bounds of approximations by de la Vallée-Poussin sums in the uniform metric. Asymptotic equalities are also obtained for the case of approximation by de la Vallée-Poussin sums in the metrics of the spaces $L_s , 1 ≤ s ≤ ∞$, on the classes of Poisson integrals of functions belonging to the unit ball of the space $L_1$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 12, pp 1941-1957.

Citation Example: Serdyuk A. S. Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics // Ukr. Mat. Zh. - 2010. - 62, № 12. - pp. 1672–1686.

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