Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 145-150
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L. D. Gogoladze. The question of $A^*$-summability of double trigonometric Fourier series. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 145-150. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a2/
@article{MZM_1972_11_2_a2,
author = {L. D. Gogoladze},
title = {The question of $A^*$-summability of double trigonometric {Fourier} series},
journal = {Matemati\v{c}eskie zametki},
pages = {145--150},
year = {1972},
volume = {11},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a2/}
}
TY - JOUR
AU - L. D. Gogoladze
TI - The question of $A^*$-summability of double trigonometric Fourier series
JO - Matematičeskie zametki
PY - 1972
SP - 145
EP - 150
VL - 11
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a2/
LA - ru
ID - MZM_1972_11_2_a2
ER -
%0 Journal Article
%A L. D. Gogoladze
%T The question of $A^*$-summability of double trigonometric Fourier series
%J Matematičeskie zametki
%D 1972
%P 145-150
%V 11
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a2/
%G ru
%F MZM_1972_11_2_a2
It is proved that for any $f(x, y)\in L(R)$, where $R=[-\pi,\pi,-\pi,\pi]$, a function $\varphi(x, y)$, exists such that $|\varphi(x,y)|=|f(x,y)|$ for almost all $(x,y)\in R$. The Fourier series of the function $\varphi(x,y)$ and all conjugate trigonometric series are $A^*$-summable almost everywhere.
