Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 777-788
Citer cet article
I. L. Bloshanskii. On the convergence of double Fourier series of functions from $L_p$, $p>1$. Matematičeskie zametki, Tome 21 (1977) no. 6, pp. 777-788. http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a4/
@article{MZM_1977_21_6_a4,
author = {I. L. Bloshanskii},
title = {On the convergence of double {Fourier} series of functions from $L_p$, $p>1$},
journal = {Matemati\v{c}eskie zametki},
pages = {777--788},
year = {1977},
volume = {21},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a4/}
}
TY - JOUR
AU - I. L. Bloshanskii
TI - On the convergence of double Fourier series of functions from $L_p$, $p>1$
JO - Matematičeskie zametki
PY - 1977
SP - 777
EP - 788
VL - 21
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a4/
LA - ru
ID - MZM_1977_21_6_a4
ER -
%0 Journal Article
%A I. L. Bloshanskii
%T On the convergence of double Fourier series of functions from $L_p$, $p>1$
%J Matematičeskie zametki
%D 1977
%P 777-788
%V 21
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1977_21_6_a4/
%G ru
%F MZM_1977_21_6_a4
It is proved that if a function from $L_p$, $p>1$, satisfies the condition $$ \frac1{t\cdot\tau}\int_0^t\int_0^\tau|f(x+u,y+v)-f(x,y)|\,du\,dv=O\Bigl(\Bigl[\ln\frac1{t^2+\tau^2}\Bigr]^{-2}\Bigr), $$ then the double Fourier series of function $f$, under summation over a rectangle, converges almost everywhere.
