Geodesic
The convergence of trigonometric series to functions of bounded variation
Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 47-58.

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Necessary and sufficient conditions are derived for the convergence of a trigonometric series to a function of bounded variation on the interval $(\alpha,\beta)\subset[-\pi,\pi]$. For the case in which the coefficients satisfy certain conditions, the continuity of the sum function is investigated. 
@article{MZM_1970_8_1_a5,
     author = {K. I. Oskolkov},
     title = {The convergence of trigonometric series to functions of bounded variation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {47--58},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a5/}
}
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K. I. Oskolkov. The convergence of trigonometric series to functions of bounded variation. Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 47-58. http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a5/