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Ukrainian Mathematical Journal

, Volume 62, Issue 7, pp 1139–1157 | Cite as

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

  • A. S. Serdyuk
  • I. V. Sokolenko
Article

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.

Keywords

Approximation Theory Linear Method Ukrainian National Academy Asymptotic Equality Minkowski Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • A. S. Serdyuk
    • 1
  • I. V. Sokolenko
    • 1
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine

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