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. 
@article{IM2_1973_7_2_a9,
     author = {B. I. Golubov},
     title = {The asymptotic $L_p$-norm of differentiated {Fourier} sums of functions of bounded variation},
     journal = {Izvestiya. Mathematics },
     pages = {401--423},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a9/}
}
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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/