Advertisement

Siberian Mathematical Journal

, Volume 60, Issue 4, pp 624–635 | Cite as

Estimate for the Entropy Numbers of the Weighted Hardy Operators that Act from Banach Space to q-Banach Space

  • E. N. LomakinaEmail author
  • M. G. NasyrovaEmail author
Article

Abstract

We study weighted Hardy operators from the Banach space Lp to the q-Banach space Lq and obtain estimates for the entropy numbers of one- and two-weighted Hardy operators with nonnegative measurable weight functions.

Keywords

integral operator Hardy operator entropy number approximation number 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Edmunds D. E. and Triebel H., Function Spaces, Entropy Numbers, Differential Operators, Cambridge Univ. Press, Cambridge (1996).CrossRefzbMATHGoogle Scholar
  2. 2.
    Prokhorov D. V., Stepanov V. D., and Ushakova E. P., “Hardy-Steklov integral operators,” Proc. Steklov Inst. Math., vol. 300, suppl. 2, 1–112 (2018).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Edmunds D. E., Evans W. D., and Harris D. J., “Approximation numbers of certain Volterra integral operators,” J. Lond. Math. Soc., vol. 38, 471–489 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Edmunds D. E., Evans W. D., and Harris D. J., “Two-sided estimates of the approximation numbers of certain Volterra integral operators,” Stud. Math., vol. 124, 59–80 (1997).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Lomakina E. and Stepanov V., “On asymptotic behaviour of the approximation numbers and estimates of Schatten-von Neumann norms of Hardy-type integral operators,” in: Function Spaces and Applications, Narosa Publ. House, New Delhi, 2000, 153–187.Google Scholar
  6. 6.
    Lifshits M. A. and Linde W., “Approximation and entropy numbers of Volterra operators with application to Brownian motion,” Mem. Amer. Math. Soc., vol. 745, 1–87 (2002).MathSciNetzbMATHGoogle Scholar
  7. 7.
    Lomakina E. N., “Asymptotic estimates for approximation numbers of the Hardy operator in q-Banach spaces,” Math. Inequal. Appl., vol. 12, no. 4, 815–825 (2009).MathSciNetzbMATHGoogle Scholar
  8. 8.
    Vasil’eva A. A., “Entropy numbers of embedding operators for weighted Sobolev spaces,” Math. Notes, vol. 98, no. 6, 982–985 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Vasil’eva A. A., “Kolmogorov widths and approximation numbers of Sobolev classes with singular weights,” St. Petersburg Math. J., vol. 24, no. 1, 1–27 (2013).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Carl B., “Entropy numbers of diagonal operators with application to eigenvalue problems,” J. Approx. Theory, vol. 32, 135–150 (1981).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Carl B. and Stephani I., Entropy, Compactness and the Approximation of Operators, Cambridge Univ. Press, Cambridge (1990).CrossRefzbMATHGoogle Scholar
  12. 12.
    Pietsch A., Operator Ideals, VEB Deutscher Verlag der Wissenschaften, Berlin (1978).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Khabarovsk State University of Economics and LawFar Eastern State Transport UniversityKhabarovskRussia
  2. 2.Computing Center of the Far Eastern Branch of the Russian Academy of SciencesKhabarovskRussia

Personalised recommendations