Geodesic
The integrability of conjugate functions
Matematičeskie zametki, Tome 4 (1968) no. 4, pp. 461-465 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\varphi$. 
@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/}
}
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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/