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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 12, pp. 1672–1686, December, 2010.
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Serdyuk, A.S. Approximation of Poisson integrals by de la Valleé-Poussin sums in uniform and integral metrics. Ukr Math J 62, 1941–1957 (2011). https://doi.org/10.1007/s11253-011-0481-4
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DOI: https://doi.org/10.1007/s11253-011-0481-4