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Estimates of Semiadditive Functionals via Deviations of Steklov Functions in the Space L 2

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We establish upper estimates for nonnegative semiadditive functionals defined on the space of periodic functions L 2 in terms of deviations of Steklov functions of even order in L 2.

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References

  1. V. V. Zhuk, “On Steklov functions” [in Russian], In: Partial Differential Equations, p. 74–85, Obrazovanie, St.-Petersburg (1992).

  2. E. G. Lanina, “The best approximations of functions and approximations by Steklov functions” [in Russian], Vestn. Mosk. Univ., Ser. I No. 2, 49–51 (2000); English transl.: Mosc. Univ. Math. Bull. 55, No. 2, 36–39 (2000).

  3. Z. Ditzian and S. Yu. Rikhonov, “Remark on the order of approximation by Steklov means” [in Russian], Vestn. Mosk. Univ., Ser. I No. 3, 57–58 (2004); English transl.: Mosc. Univ. Math. Bull. 55, No. 3, 47–48 (2004).

  4. V. A. Abilov and F. V. Abilova, “Problems in the approximation of 2π-periodic functions by Fourier sums in the space L 2(2π)” [in Russian], Mat. Zametki 76, No. 6, 803–811 (2004); Math. Notes 76, No. 6, 749–757 (2004).

  5. V. O. Dron’ and V. V. Zhuk, “Approximation of periodic functions by Steklov averages in L2” [in Russian], Probl. Math. Anal. 35, 79–89 (2007); English transl.: J. Math. Sci., New York 144, No. 6, 4612–4623 (2007).

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Authors and Affiliations

  1. St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia

    V. V. Zhuk & A. A. Pudovkin

Authors
  1. V. V. Zhuk
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  2. A. A. Pudovkin
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Correspondence to V. V. Zhuk.

Additional information

Translated from Problemy Matematicheskogo Analiza 87, October 2016, pp. 129-134.

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Zhuk, V.V., Pudovkin, A.A. Estimates of Semiadditive Functionals via Deviations of Steklov Functions in the Space L 2 . J Math Sci 219, 967–972 (2016). https://doi.org/10.1007/s10958-016-3158-6

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  • DOI: https://doi.org/10.1007/s10958-016-3158-6

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