Uniform approximation of Poisson integrals of functions from the class Hω by de la Vallée Poussin sums
@article{Serdyuk2012UniformAO,
title={Uniform approximation of Poisson integrals of functions from the class Hω by de la Vall{\'e}e Poussin sums},
author={A. Serdyuk and Ie.Yu. Ovsii},
journal={Analysis Mathematica},
year={2012},
volume={38},
pages={305-325}
}We obtain asymptotic equalities for least upper bounds of deviations in the uniform metric of de la Vallée Poussin sums on the sets CβqHω of Poisson integrals of functions from the class Hω generated by convex upwards moduli of continuity ω(t) which satisfy the condition ω(t)/t → ∞ as t → 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 Hα, 0 < α < 1, is obtained… CONTINUE READING
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