Geodesic
On the convergence of conjugate Fourier series
Izvestiya. Mathematics , Tome 2 (1968) no. 1, pp. 47-59.

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We investigate the convergence of the series which is conjugate to the Fourier series of a function $f(x)$, when the measure of the continuity of $f(x)$ is given in the mean. 
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M. A. Subkhankulov. On the convergence of conjugate Fourier series. Izvestiya. Mathematics , Tome 2 (1968) no. 1, pp. 47-59. http://geodesic.mathdoc.fr/item/IM2_1968_2_1_a2/

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