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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     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},
     publisher = {mathdoc},
     volume = {99},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_6_a6/}
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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/