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 Mat. Zametki, 2016, Volume 99, Issue 6, Pages 878–886 (Mi mz10960)

On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$

M. R. Gabdullinab

a Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: 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 $L^p$, $p\in(0,1)$, convergence of Fourier series, integrable function.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 02.A03.21.0006 This work was supported by the Program of State Support for Leading Universities of the Russian Federation under cintract 02. A03.21.0006 of August 27, 2013.

DOI: https://doi.org/10.4213/mzm10960

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English version:
Mathematical Notes, 2016, 99:6, 861–869

Bibliographic databases:

UDC: 517
Revised: 18.10.2015

Citation: M. R. Gabdullin, “On the Divergence of Fourier Series in the Spaces $\varphi(L)$ Containing $L$”, Mat. Zametki, 99:6 (2016), 878–886; Math. Notes, 99:6 (2016), 861–869

Citation in format AMSBIB
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