Geodesic
Estimates of the Sums of Sine Series with Monotone Coefficients of Certain Classes
Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 877-888

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In this paper, we obtain two-sided estimates with sharp constants of the sums of sine series with a convex sequence of coefficients tending to zero. 
@article{MZM_2003_74_6_a7,
     author = {A. Yu. Popov},
     title = {Estimates of the {Sums} of {Sine} {Series} with {Monotone} {Coefficients} of {Certain} {Classes}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {877--888},
     publisher = {mathdoc},
     volume = {74},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a7/}
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A. Yu. Popov. Estimates of the Sums of Sine Series with Monotone Coefficients of Certain Classes. Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 877-888. http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a7/