Geodesic
Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs
Ural mathematical journal, Tome 3 (2017) no. 2, pp. 46-50

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We consider certain classes of functions with a restriction on the fractality of their graphs. Modifying Lebesgue's example, we construct continuous functions from these classes whose Fourier series diverge at one point, i.e. the Fourier series of continuous functions from this classes do not converge everywhere.
Keywords: Trigonometric Fourier series, Fractality, Сontinuous functions.
Mots-clés : Divergence at one point 
Maxim L. Gridnev. Divergence of the Fourier series of continuous functions with a restriction on the fractality of their graphs. Ural mathematical journal, Tome 3 (2017) no. 2, pp. 46-50. http://geodesic.mathdoc.fr/item/UMJ_2017_3_2_a6/
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[3] Waterman D., “On converges of Fourier series of functions of generalized bounded variation”, Studia Mathematica, 44 (1972), 107–117

[4] Gridnev M. L., “About classes of functions with a restriction on the fractality of their graphs”, Proceedings of the 48th Intern. Youth School-Conf.: Modern Problems in Mathematics and its Applications (Ekaterinburg, February 5–11, 2017), CEUR-WS Proceedings, 1894, 2017, 167–3 (in Russian) http://ceur-ws.org/Vol-1894/appr5.pdf