Skip to main content
SpringerLink
Log in

Relation between moduli of smoothness and partial sums of Fourier series and embedding theorems for Nikol’skii classes

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

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

References

  1. S. M. Nikol’skii, Approximation of Functions of Several Variables and Imbedding Theorems (Springer-Verlag, New York, 1975; Nauka, Moscow, 1977).

    Google Scholar 

  2. S. M. Nikol’skii, Dokl. Akad. Nauk SSSR 52, 191–194 (1946).

    Google Scholar 

  3. S. B. Stechkin, Izv. Akad. Nauk, Ser. Mat. 15, 219–242 (1951).

    MATH  Google Scholar 

  4. S. M. Nikol’skii, Dokl. Akad. Nauk 60, 1507–1510 (1948).

    Google Scholar 

  5. R. Taberski, Comment. Math. 19, 389–400 (1977).

    MathSciNet  Google Scholar 

  6. V. G. Ponomarenko, “Fractional-Order Moduli of Smoothness and Best Approximations Constructive Function Theory,” Proceedings of International Conference (Varna, 1981), pp. 129–133.

  7. B. V. Simonov, On the Properties of Transformed Fourier Series, Available from VINITI, No. 3031-61 (Moscow, 1981).

  8. M. K. Potapov and B. V. Simonov, Anal. Math. 22, 299–316 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  9. S. M. Nikol’skii, Sib. Mat. Zh., No. 4, 1342–1365 (1963).

  10. O. V. Besov, V. P. Il’in, and S. M. Nikol’skii, Integral Representations of Functions and Imbedding Theorems (Nauka, Moscow, 1975; Wiley, New York, 1978).

    Google Scholar 

  11. M. K. Potapov, B. V. Simonov, and S. Yu. Tikhonov, Proc. Steklov Inst. Math. 269, 197–207 (2010) [Tr. Mat. Inst. im. V.A. Steklova, Ross. Akad. Nauk 269, 204–214 (2010)].

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Volgograd State Technical University, pr. Lenina 28, Volgograd, 400131, Russia

    B. V. Simonov

Authors
  1. B. V. Simonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. V. Simonov.

Additional information

Original Russian Text © B.V. Simonov, 2011, published in Doklady Akademii Nauk, 2011, Vol. 437, No. 6, pp. 751–753.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Simonov, B.V. Relation between moduli of smoothness and partial sums of Fourier series and embedding theorems for Nikol’skii classes. Dokl. Math. 83, 265–267 (2011). https://doi.org/10.1134/S1064562411020347

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562411020347

Keywords

Search

Navigation