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. 
@article{TRSPY_2013_283_a15,
     author = {S. A. Telyakovskii},
     title = {Boundedness of the series of absolute values of blocks of sine series},
     journal = {Informatics and Automation},
     pages = {252--256},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2013_283_a15/}
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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/