Skip to main content
SpringerLink
Log in

Fourier coefficients of functions from many-dimensional classes of bounded Λ-variation

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

Estimates of trigonometric Fourier coefficients are obtained for functions from the classes of bounded many-dimensional Λ-variation and functions continuous in Λ-variation. In some cases it is proved that these estimates are unimprovable by the order.

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. D. Waterman, “On Convergence of Fourier Series of Functions of Generalized Bounded Variation,” Stud. math. 44(1), 107 (1972).

    MATH  MathSciNet  Google Scholar 

  2. A. A. Saakyan, “Convergence of Double Fourier Series of Functions of Bounded Harmonic Variation,” Izv. Akad. Nauk Arm. SSR 21(6), 517 (1986).

    MATH  MathSciNet  Google Scholar 

  3. A. I. Sablin, “Λ-Variation and Fourier Series,” Izv. Vuzov. Matem. No. 10, 66 (1987).

  4. A. N. Bakhvalov, “Continuity in Λ-Variation of Functions of Several Variables and Convergence of Multiple Fourier Series,” Matem. Sbornik 193(12), 3 (2002) [Sbornik: Math. 193 (12), 1731 (2002)].

    MathSciNet  Google Scholar 

  5. D. Waterman “On the Summability of Fourier Series of Functions of Λ-Bounded Variation,” Stud. math. 55(1), 87 (1976).

    MATH  Google Scholar 

  6. O. S. Dragoshanskii, “Continuity in Λ-Variations of Functions of Several Variables,” Matem. Sbornik 194(7), 57 (2003) [Sbornik: Math. 194 (7), 1009 (2003)].

    MathSciNet  Google Scholar 

  7. M. Schramm and D. Waterman, “On the Magnitude of Fourier Coefficients,” Proc. Amer. Math. Soc. 85(3), 408 (1982).

    Article  MathSciNet  Google Scholar 

  8. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities (Cambridge University Press, London, 1934; IL, Moscow, 1948).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119899, Russia

    A. N. Bakhvalov

Authors
  1. A. N. Bakhvalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.N. Bakhvalov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 1, pp. 10–18.

About this article

Cite this article

Bakhvalov, A.N. Fourier coefficients of functions from many-dimensional classes of bounded Λ-variation. Moscow Univ. Math. Bull. 66, 8–16 (2011). https://doi.org/10.3103/S0027132211010025

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132211010025

Keywords

Search

Navigation