Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 63-77
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S. V. Konyagin. Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere. Matematičeskie zametki, Tome 52 (1992) no. 3, pp. 63-77. http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a6/
@article{MZM_1992_52_3_a6,
author = {S. V. Konyagin},
title = {Convergence of subsequences of partial cubic sums of {Fourier} series in mean and almost everywhere},
journal = {Matemati\v{c}eskie zametki},
pages = {63--77},
year = {1992},
volume = {52},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a6/}
}
TY - JOUR
AU - S. V. Konyagin
TI - Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere
JO - Matematičeskie zametki
PY - 1992
SP - 63
EP - 77
VL - 52
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a6/
LA - ru
ID - MZM_1992_52_3_a6
ER -
%0 Journal Article
%A S. V. Konyagin
%T Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere
%J Matematičeskie zametki
%D 1992
%P 63-77
%V 52
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1992_52_3_a6/
%G ru
%F MZM_1992_52_3_a6
Under certain assumptions on the regularity of a function $\Phi$ necessary and sufficient conditions are found for $\Phi$ under which the integrability of $\Phi(|f|)$ implies, for every function $f$ measurable on $T^d$, the existence of a subsequence of cubic sums of the Fourier series of $f$ that converges to f in mean or almost everywhere.
