Mathematical Notes

, Volume 99, Issue 5–6, pp 861–869 | Cite as

On the divergence of Fourier series in the spaces ϕ(L) containing L

  • M. R. Gabdullin
Short Communications


The paper deals with the question of the divergence of Fourier series in function spaces wider than L = L[−π, π], but narrower than L p = L p [−π, π] for all p ∈ (0, 1). It is proved that the recent results of Filippov on the generalization to the space ϕ(L) of Kolmogorov’s theorem on the convergence of Fourier series in L p , p ∈ (0, 1), cannot be improved.


Fourier series the space ϕ(Lthe spaces Lp p ∈ (0 1) convergence of Fourier series integrable function 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. K. Bari, Trigonometric Series (Fizmatgiz, Moscow, 1961) [in Russian].Google Scholar
  2. 2.
    A. Kolmogoroff, “Sur les fonctions harmoniques conjuguées et les séries de Fourier,” Fundamenta 7, 24–29 (1925).MATHGoogle Scholar
  3. 3.
    V. I. Filippov, “On the Kolmogorov theorems on Fourier series and conjugate functions,” Izv. Vyssh. Uchebn. Zaved.Mat., No. 7, 21–34 (2012) [Russian Math. (Iz. VUZ) 56 (7), 18–29 (2012)].MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Mathematics and Computer ScienceUral Federal UniversityEkaterinburgRussia
  2. 2.Krasovskii Institute of Mathematics and Mechanics, Ural DivisionRussian Academy of SciencesEkaterinburgRussia

Personalised recommendations