Geodesic
Conjugate functions and the restricted Denjoy integral
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 81-124

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We study the functions conjugate to Denjoy integrable functions. In particular, it is shown that if $f$ and its conjugate $\overline f$ are integrable in the restricted Denjoy sense then the conjugate series coincides with the Fourier–Denjoy series of the conjugate function, $(D^*)\sigma[\overline f]=(D^*)\overline\sigma [f]$, and the Riesz equation $(D^*)\int_0^{2\pi}\varphi\overline f\,dx=-(D^*)\int_0^{2\pi}f\overline\varphi\,dx$ holds provided that $\varphi$ and its conjugate function $\overline\varphi$ are of bounded variation. Bibliography: 20 titles. 
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     author = {T. P. Lukashenko},
     title = {Conjugate functions and the restricted {Denjoy} integral},
     journal = {Sbornik. Mathematics},
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     number = {1},
     year = {1977},
     language = {en},
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T. P. Lukashenko. Conjugate functions and the restricted Denjoy integral. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 81-124. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a5/