Geodesic
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.

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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. 
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     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},
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     publisher = {mathdoc},
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     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a2/}
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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/