Geodesic
A~Fourier series in an arbitrary bounded orthonormal system that diverges on a~set of positive measure
Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 393-405

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It is shown that every system of collectively bounded orthonormal functions admits an integrable function whose Fourier series diverges on a set of positive measure. Bibliography: 6 titles. 
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     title = {A~Fourier series in an arbitrary bounded orthonormal system that diverges on a~set of positive measure},
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S. V. Bochkarev. A~Fourier series in an arbitrary bounded orthonormal system that diverges on a~set of positive measure. Sbornik. Mathematics, Tome 27 (1975) no. 3, pp. 393-405. http://geodesic.mathdoc.fr/item/SM_1975_27_3_a5/