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Inequalities for upper bounds of functionals on the classes w r H ω and their applications

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Abstract

We show that the well-known results on estimates of upper bounds of functionals on the classes W r Hω of periodic functions can be regarded as a special case of Kolmogorov-type inequalities for support functions of convex sets. This enables us to prove numerous new statements concerning the approximation of the classes W r Hω, establish the equivalence of these statements, and obtain new exact inequalities of the Bernstein-Nikol’skii type that estimate the value of the support function of the class H ω on the derivatives of trigonometric polynomials or polynomial splines in terms of the L ϱ-norms of these polynomials and splines.

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Authors and Affiliations

  1. Academician, Ukrainian Academy of Sciences. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    N. P. Korneichuk

  2. Dnepropetrovsk University, Dnepropetrovsk

    V. F. Babenko, V. A. Kofanov & S. A. Pichugov

Authors
  1. N. P. Korneichuk
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  2. V. F. Babenko
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  3. V. A. Kofanov
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  4. S. A. Pichugov
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Korneichuk, N.P., Babenko, V.F., Kofanov, V.A. et al. Inequalities for upper bounds of functionals on the classes w r H ω and their applications. Ukr Math J 52, 71–90 (2000). https://doi.org/10.1007/BF02514138

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  • DOI: https://doi.org/10.1007/BF02514138

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