Ukrainian Mathematical Journal

, Volume 67, Issue 11, pp 1786–1792 | Cite as

Kolmogorov Widths for Analogs of the Nikol’skii–Besov Classes with Logarithmic Smoothness

  • S. A. Stasyuk

We establish the exact-order estimates of Kolmogorov widths and entropy numbers for analogs of the Nikol’skii–Besov classes with logarithmic smoothness.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. S. Kashin and V. N. Temlyakov, “On one norm and approximating characteristics of the classes of functions of many variables,” Teor. Funkts., Ser. Fiz.-Mat. Nauk, 25, 58–79 (2007).Google Scholar
  2. 2.
    A. Seeger and W. Trebels, “Low regularity classes and entropy numbers,” Arch. Math., 92, No. 2, 147–157 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    S. A. Stasyuk, “Approximating characteristics of the analogs of Besov classes with logarithmic smoothness,”Ukr. Mat. Zh., 66, No. 4, 493–499 (2014); English translation: Ukr. Math. J., 66, No. 4, 553–560 (2014).Google Scholar
  4. 4.
    F. Cobos and Ó. Domínquez, “On Besov spaces of logarithmic smoothness and Lipschitz spaces,” J. Math. Anal. Appl., 425, No. 1, 71–84 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    A. Pietsch, Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).zbMATHGoogle Scholar
  6. 6.
    V. N. Temlyakov, Approximation of Periodic Functions, Nova Science Publ., New York (1993).zbMATHGoogle Scholar
  7. 7.
    A. S. Romanyuk, Approximating Characteristics of the Classes of Periodic Functions of Many Variables [in Ukrainian], Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2012).Google Scholar
  8. 8.
    A. S. Romanyuk, “Estimates of the entropy numbers and ε-entropy for the classes of periodic functions of many variables,” in: Approximation Theory of Functions and Related Problems [in Ukrainian], Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, 11, No. 3 (2014), pp. 196–213.Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • S. A. Stasyuk
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

Personalised recommendations