Geodesic
Denjoy--Khinchin-integrable functions and their conjugates
Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 625-664

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In this paper $2\pi$-periodic functions $\Phi(x)$ and $\Psi(x)$ are constructed so that they are both Denjoy–Khinchin integrable, are not equivalent to zero, and have conjugates $\overline\Phi$ and $\overline\Psi$ satisfying $\overline\Phi(x)=0$ almost everywhere and $\overline\Psi(x)=1$ almost everywhere. Bibliography: 12 titles. 
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     author = {T. P. Lukashenko},
     title = {Denjoy--Khinchin-integrable functions and their conjugates},
     journal = {Izvestiya. Mathematics },
     pages = {625--664},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a8/}
}
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T. P. Lukashenko. Denjoy--Khinchin-integrable functions and their conjugates. Izvestiya. Mathematics , Tome 11 (1977) no. 3, pp. 625-664. http://geodesic.mathdoc.fr/item/IM2_1977_11_3_a8/