Geodesic
On the Rate of Convergence in~$L$ of Fourier Sine Series with Monotone Coefficients
Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 450-454

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It is shown that the exact order of decrease of the norm in $L$ of the remainder of a Fourier sine series with monotone coefficients can be expressed in terms of the coefficients of the series just as for a series with convex coefficients. But the numerical multipliers in the estimates are different.
Mots-clés : convergence in $L$
Keywords: sine series with monotone coefficients. 
@article{MZM_2016_100_3_a11,
     author = {S. A. Telyakovskii},
     title = {On the {Rate} of {Convergence} in~$L$ of {Fourier} {Sine} {Series} with {Monotone} {Coefficients}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {450--454},
     publisher = {mathdoc},
     volume = {100},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a11/}
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S. A. Telyakovskii. On the Rate of Convergence in~$L$ of Fourier Sine Series with Monotone Coefficients. Matematičeskie zametki, Tome 100 (2016) no. 3, pp. 450-454. http://geodesic.mathdoc.fr/item/MZM_2016_100_3_a11/