Skip to main content
Log in

Strong summability of fourier series on classes of (ψ, β)-differentiable functions

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Literature cited

  1. G. H. Hardy and J. E. Littlewood, “Sur la serie de Fourier d'une fonction á carre sommable,” Comput. Rev.,153, 1307–1309 (1913).

    Google Scholar 

  2. G. H. Hardy and J. E. Littlewood, “On the strong summability of Fourier series,” Proc. London Math. Soc,26, 273–286 (1926).

    Google Scholar 

  3. A. I. Stepanets, “Classes of periodic functions and approximation of their elements by sums,” Dokl. Akad. Nauk SSSR,277, No. 5, 1074–1077 (1984).

    Google Scholar 

  4. A. I. Stepanets, “Classification of periodic functions and the rate of convergence of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 1, 101–136 (1986).

    Google Scholar 

  5. A. I. Stepanets, “Deviations of Fourier sums on the classes of infinitely differentiable functions,” Ukr. Mat. Zh.,36, No. 6, 750–758 (1984).

    Google Scholar 

  6. A. I. Stepanets, “Approximation of the functions with slowly decreasing Fourier coefficients by Fourier sums,” Ukr. Mat. Zh.,38, No. 6, 755–762 (1986).

    Google Scholar 

  7. K. I. Oskolkov, “On the Lebesgue inequality in the uniform metric and on a set of full measure,” Mat. Zametki,18, No. 4, 515–526 (1975).

    Google Scholar 

  8. V. A. Baskakov, “On the approximation of the function classes C(ɛ) by the ValléePoussin sums and by linear polynomial operators,” Izv. Vyssh. Uchebn. Zaved., No. 5, 19–24 (1984).

    Google Scholar 

  9. L. D. Gogoladze, “On the strong summability of simple and multiple trigonometric Fourier series,” in: Certain Questions of Theory of Functions [in Russian], Vol. 2, Tbilisi State Univ. (1981), pp. 5–50.

  10. A. I. Stepanets and A. K. Kushpel', The Best Approximations and the Widths of Classes of Periodic Functions [in Russian], Preprint No. 84.15, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1984).

    Google Scholar 

  11. A. I. Stepanets and N. L. Pachulia, On the Strong Summability of Fourier Series [in Russian], Preprint No. 86.61, Inst. Akad. Nauk SSR, Kiev (1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 44, No. 4, pp. 506–516, October, 1988.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pachulia, N.L., Stepanets, A.I. Strong summability of fourier series on classes of (ψ, β)-differentiable functions. Mathematical Notes of the Academy of Sciences of the USSR 44, 758–764 (1988). https://doi.org/10.1007/BF01158920

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01158920

Keywords

Navigation