Skip to main content
SpringerLink
Log in

Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L p -space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. É. N. Batuev and V.D. Stepanov, “Weighted Inequalities of Hardy Type,” Sibirsk. Mat. Zh. 30(1), 13–22 (1989) [Siberian Math. J. 30 (1), 8–16 (1989)].

    MathSciNet  Google Scholar 

  2. V. D. Stepanov, “Two-Weight Estimates for Riemann-Liouville Integrals,” Izv. Akad. Nauk SSSR Ser. Mat. 54(3), 645–655 (1990) [Math.-USSR-Izv. 36 (3), 669–681 (1991)].

    MATH  Google Scholar 

  3. V. D. Stepanov, “Two-Weighted Estimates for Riemann-Liouville Integrals,” Rept. 39, Ceskoslov. Akad. Věd. Mat. Ústav. (Praha, 1988).

  4. V. D. Stepanov, “Weighted Norm Inequalities for Integral Operators and Related Topics,” in Nonlinear Analysis, Function Spaces and Applications, Proceedings of the Spring School Held in Prague, May 23–28, 1994, Vol. 5, Ed. by M. Krbec, A. Kufner, B. Opic, and J. Rakosnik (Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha, 1995), pp. 139–175.

    Google Scholar 

  5. V. D. Stepanov, “Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators,” J. London Math. Soc. 50(1), 105–120 (1994).

    MATH  MathSciNet  Google Scholar 

  6. N. P. Korneichuk, Splines in Approximation Theory (Nauka, Moscow, 1984) [in Russian].

    Google Scholar 

  7. G. G. Lorentz, Approximation of Functions (Hdt Rinehart, Winston, New York, 1966).

    MATH  Google Scholar 

  8. A. Pinkus, n-Widths in Approximation Theory (Springer, Berlin: 1985).

    MATH  Google Scholar 

  9. V. M. Tikhomirov, Some Questions in Approximation Theory (Izdat. Moskov. Univ., Moscow, 1976).

    Google Scholar 

  10. V. M. Tikhomirov, “Approximation Theory,” in Current Problems in Mathematics. Fundamental Directions 14 (Itogi Nauki i Tekhniki) (Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987), pp. 103–260.

    Google Scholar 

  11. Yu. [Ju.] I. Makovoz, “A Certain Method of Obtaining Lower Estimates for Diameters of Sets in Banach Spaces,” Mat. Sb. 87(129) (1), 136–142 (1972).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    A. A. Vasil’eva

Authors
  1. A. A. Vasil’eva
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the program “Leading Scientific Schools” (grant no. NSh-3233.2008.1).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vasil’eva, A.A. Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis. Russ. J. Math. Phys. 16, 543–562 (2009). https://doi.org/10.1134/S1061920809040098

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920809040098

Keywords

Search

Navigation