Geodesic
On functions of generalized bounded variation
Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 267-301

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A theorem is proved on passage to a limit under the sign of a Perron–Stieltjes integral, and it is used to obtain several other theorems, one of which is the following. Theorem. If $\Phi$ and its conjugate $\overline\Phi$ are functions of generalized bounded variation in the narrow sense on $[0,2\pi)$ that do not have discontinuities of the second kind nor removable discontinuities (that is, left-hand and right-hand limits exist at each point, and they do not coincide at a point of discontinuity), then $\Phi$ and $\overline\Phi$ are absolutely continuous functions in the generalized narrow sense on $[0,2\pi)$. It is shown that the results cannot be strengthened. Bibliography: 14 titles. 
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     author = {T. P. Lukashenko},
     title = {On functions of generalized bounded variation},
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T. P. Lukashenko. On functions of generalized bounded variation. Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 267-301. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a4/