Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 269-280
Citer cet article
L. V. Zhizhiashvili. A generalization of a theorem of M. Riesz to the case of functions of several variables. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 269-280. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a2/
@article{MZM_1968_4_3_a2,
author = {L. V. Zhizhiashvili},
title = {A generalization of a theorem of {M.~Riesz} to the case of functions of several variables},
journal = {Matemati\v{c}eskie zametki},
pages = {269--280},
year = {1968},
volume = {4},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a2/}
}
TY - JOUR
AU - L. V. Zhizhiashvili
TI - A generalization of a theorem of M. Riesz to the case of functions of several variables
JO - Matematičeskie zametki
PY - 1968
SP - 269
EP - 280
VL - 4
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a2/
LA - ru
ID - MZM_1968_4_3_a2
ER -
%0 Journal Article
%A L. V. Zhizhiashvili
%T A generalization of a theorem of M. Riesz to the case of functions of several variables
%J Matematičeskie zametki
%D 1968
%P 269-280
%V 4
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a2/
%G ru
%F MZM_1968_4_3_a2
The following theorem was proved by M. Riesz: If $f(x)\in L(-\pi,\pi)$, $f(x)\geqslant0$ and the conjugate function $f(x)$ is also integrable on $[-\pi,\pi]$, then $f(x)\in L\log^+L$. The analog of this theorem for functions of several variables is established.
