Matematičeskie zametki, Tome 4 (1968) no. 4, pp. 461-465
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O. D. Tsereteli. The integrability of conjugate functions. Matematičeskie zametki, Tome 4 (1968) no. 4, pp. 461-465. http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a9/
@article{MZM_1968_4_4_a9,
author = {O. D. Tsereteli},
title = {The integrability of conjugate functions},
journal = {Matemati\v{c}eskie zametki},
pages = {461--465},
year = {1968},
volume = {4},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a9/}
}
TY - JOUR
AU - O. D. Tsereteli
TI - The integrability of conjugate functions
JO - Matematičeskie zametki
PY - 1968
SP - 461
EP - 465
VL - 4
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a9/
LA - ru
ID - MZM_1968_4_4_a9
ER -
%0 Journal Article
%A O. D. Tsereteli
%T The integrability of conjugate functions
%J Matematičeskie zametki
%D 1968
%P 461-465
%V 4
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1968_4_4_a9/
%G ru
%F MZM_1968_4_4_a9
For any function $f$ of $L(0,2\pi)$, we prove that there is a function $\varphi\in L(0,2\pi)$ such that $|\varphi(x)|=|f(x)|$ almost everywhere and $\tilde{\varphi}\in L(0,2\pi)$, where $\tilde{\varphi}$ is the conjugate of $\varphi$.
