2017
Том 69
№ 9

All Issues

Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p}$ in the metrics of the spaces $L_p$

Serdyuk A. S., Sokolenko I. V.

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Abstract

We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from $H_{ω_p}$ for $1 ≤ p < ∞$ by a certain linear method $U_n^{*}$ in the metric of the space $L_p$. It is shown that the obtained estimates are asymptotically exact for $р = 1$: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from $H_{ω_1}$ in the metric of the space $L_1$ and show that, for these classes, the method $U_n^{*}$ is the best polynomial approximation method in a sense of strong asymptotic behavior.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1139-1157.

Citation Example: Serdyuk A. S., Sokolenko I. V. Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes $H_{ω_p}$ in the metrics of the spaces $L_p$ // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 979–996.

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