Abstract

We study how the well-known criterion for the uniform convergence of a sine series with monotone coefficients changes if, instead of monotonicity, one imposes the condition of \(\alpha\)-monotonicity with \(0<\alpha <1\). Moreover, we obtain an addition to the well-known Kolmogorov theorem on the integrability of the sum of a cosine series with convex coefficients tending to zero.

中文翻译：

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具有分数单调系数的正弦级数的一致收敛性

摘要

我们研究如果不采用单调性，而是施加\(\alpha\) -单调性且\(0<\alpha <1\)的条件，则具有单调系数的正弦级数一致收敛的众所周知的准则将如何变化。此外，我们还得到了著名的柯尔莫哥洛夫定理关于凸系数趋于零的余弦级数之和的可积性的补充。