Geodesic
Boundedness of the series of absolute values of blocks of sine series
Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 252-256.

Voir la notice de l'article provenant de la source Math-Net.Ru

The series of absolute values of blocks of a sine series whose coefficients satisfy a certain weakened monotonicity condition are considered. It is shown that to ensure the bounded convergence of such a series, one can take the same blocks as for the Fourier series of functions of bounded variation. 
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S. A. Telyakovskii. Boundedness of the series of absolute values of blocks of sine series. Informatics and Automation, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 252-256. http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a15/

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