Geodesic
On the Divergence of Fourier Series in the Spaces~$\varphi(L)$ Containing~$L$
Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 878-886.

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The paper deals with the question of the divergence of Fourier series in function spaces wider than $L=L[-\pi,\pi]$, but narrower than $L^p=L^p[-\pi,\pi]$ for all $p\in(0,1)$. It is proved that the recent results of Filippov on the generalization to the space $\varphi(L)$ of Kolmogorov's theorem on the convergence of Fourier series in $L^p$, $p\in(0,1)$, cannot be improved.
Keywords: Fourier series, the space $\varphi(L)$, the spaces $L^p$, $p\in(0,1)$, integrable function.
Mots-clés : convergence of Fourier series 
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M. R. Gabdullin. On the Divergence of Fourier Series in the Spaces~$\varphi(L)$ Containing~$L$. Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 878-886. http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a6/

[1] H. K. Bari, Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[2] A. Kolmogoroff, “Sur les fonctions harmoniques conjuguées et les séries de Fourier”, Fundamenta, 7 (1925), 24–29 | Zbl

[3] V. I. Filippov, “Ob usilenii rezultatov A. N. Kolmogorova o ryadakh Fure i sopryazhennykh funktsiyakh”, Izv. vuzov. Matem., 2012, no. 7, 21–34 | MR | Zbl