Geodesic
On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$
Matematičeskie zametki, Tome 99 (2016) no. 6, pp. 878-886 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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 
@article{MZM_2016_99_6_a6,
     author = {M. R. Gabdullin},
     title = {On the {Divergence} of {Fourier} {Series} in the {Spaces~}$\varphi(L)$ {Containing~}$L$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {878--886},
     year = {2016},
     volume = {99},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a6/}
}
TY  - JOUR
AU  - M. R. Gabdullin
TI  - On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$
JO  - Matematičeskie zametki
PY  - 2016
SP  - 878
EP  - 886
VL  - 99
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a6/
LA  - ru
ID  - MZM_2016_99_6_a6
ER  - 
%0 Journal Article
%A M. R. Gabdullin
%T On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$
%J Matematičeskie zametki
%D 2016
%P 878-886
%V 99
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a6/
%G ru
%F MZM_2016_99_6_a6
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