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arXiv · 1104.3060

Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums

A. S. Serdyuk·Ie. Yu. Ovsii
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Abstract

We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vallée Poussin sums on the sets C^{q}_βH_ωof Poisson integrals of functions from the class H_ωgenerated by convex upwards moduli of continuity ω(t) which satisfy the condition ω(t)/t\to\infty as t\to 0. As an implication, a solution of the Kolmogorov-Nikol'skii problem for de la Vallée Poussin sums on the sets of Poisson integrals of functions belonging to Lipschitz classes H^α, 0<α<1, is obtained

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A. S. Serdyuk, Ie. Yu. Ovsii. 2011-04-15. Uniform approximation of Poisson integrals of functions from the class H_omega by de la Vallee Poussin sums. https://doi.org/10.1007/s10476-012-0403-1

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