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Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes \( {H_{{\omega_p}}} \) in the metrics of the spaces L p

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Ukrainian Mathematical Journal Aims and scope

We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from \( {H_{{\omega_p}}} \) 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 p = 1: In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from \( {H_{{\omega_1}}} \) 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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. S. Serdyuk & I. V. Sokolenko

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  1. A. S. Serdyuk
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  2. I. V. Sokolenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 7, pp. 979–996, July, 2010.

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Serdyuk, A.S., Sokolenko, I.V. Linear approximation methods and the best approximations of the Poisson integrals of functions from the classes \( {H_{{\omega_p}}} \) in the metrics of the spaces L p . Ukr Math J 62, 1139–1157 (2010). https://doi.org/10.1007/s11253-010-0419-2

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  • DOI: https://doi.org/10.1007/s11253-010-0419-2

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