Geodesic
Integrals and $n$-dimensional conjugate functions
Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 553-589.

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We study $A$- and $B$-integrability of $n$-dimensional conjugate functions and determine when the Fourier series of the conjugate function is its conjugate series. 
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T. P. Lukashenko. Integrals and $n$-dimensional conjugate functions. Izvestiya. Mathematics , Tome 8 (1974) no. 3, pp. 553-589. http://geodesic.mathdoc.fr/item/IM2_1974_8_3_a7/

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