Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity

  • 28 Accesses

  • 3 Citations


It is proved that a quasiconvex sequenceλ v of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuityω(gd) into uniformly convergent series if and only ifλ n ω(1/n) log n → 0 for n →∞. The sufficiency of this condition is already known.

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

Literature cited

  1. 1.

    M. Tomić, “Sur les facteurs de convergence des séries de Fourier des fonctions continues,” Publ. Inst., Math. Acad. Serbe Sci.,8, 23–32 (1955).

  2. 2.

    M. Tomić, “Sur la sommation de la série de Fourier d'une fonction continue avec le module de continuité donné,” Publ. Inst. Math. Acad. Serbe Sci.,10, 19–36 (1956).

  3. 3.

    R. Bojanić, “On uniform convergence of Fourier series,” Publ. Inst. Math. Acad. Serbe Sci.,10, 153–158 (1956).

  4. 4.

    A. Kolmogoroff, “Sur l'ordre de grandeur des coefficients de la série de Fourier-Lebesgue,” Bull. Acad. Polon. Sci. (A), Sci. Math., 83–86 (1923).

  5. 5.

    A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge (1959).

  6. 6.

    H. Lebesgue, “Sur la représentation trigonométrique approchée des fonctions satisfaisant a une condition de Lipschitz,” Bull. Soc. Math. France,38, 184–210 (1910).

  7. 7.

    R. DeVore, “Multipliers of uniform convergence,” L'Enseignement Math. (2)14, No. 2, 175–188 (1969).

Download references

Author information

Additional information

Translated from Matematicheskie Zametki, Vol. 8, No. 5,pp. 619–623, November, 1970.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Telyakovskii, S.A. Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity. Mathematical Notes of the Academy of Sciences of the USSR 8, 817–819 (1970). https://doi.org/10.1007/BF01146938

Download citation


  • Fourier
  • Fourier Series
  • Convergent Series
  • Convergence Factor