Geodesic
The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation
Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 401-423.

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An asymptotic expression as $n\to\infty$ is found for the norms $\|S_n^{(r)}(x,f)\|_{L_q}$ ($1\le p$, $r=1,2,\dots$), where $S_n(x,f)$ is a Fourier sum of the $2\pi$-periodic function $f(x)$ having bounded $p$-variation. Various criteria for the continuity of a function of bounded $p$-variation are obtained as corollaries. 
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B. I. Golubov. The asymptotic $L_p$-norm of differentiated Fourier sums of functions of bounded variation. Izvestiya. Mathematics , Tome 7 (1973) no. 2, pp. 401-423. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a9/

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