Geodesic
Two-sided estimate for the derivative of the sum of sine series with convex sequence of coefficients
Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1374-1405

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The absolute value of the derivative of the sum of an arbitrary sine series with convex sequence of coefficients is estimated. The upper estimate is asymptotically sharp, and the lower estimate is order sharp. Bibliography: 13 titles.
Keywords: sine series, convex sequence of coefficients. 
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     author = {A. Yu. Popov},
     title = {Two-sided estimate for the derivative of the sum of sine series with convex sequence of coefficients},
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A. Yu. Popov. Two-sided estimate for the derivative of the sum of sine series with convex sequence of coefficients. Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1374-1405. http://geodesic.mathdoc.fr/item/SM_2024_215_10_a3/