Abstract This paper is a study of trigonometric series with general monotone coefficients in the class with . Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For two-sided estimates are obtained for the -moduli of smoothness of sums of series with -coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients. Bibliography: 99 titles.

中文翻译：

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具有一般单调傅立叶系数的函数

摘要 本文研究了一类具有一般单调系数的三角级数。对可积函数和连续函数的傅立叶系数证明了尖锐的估计。还获得了就傅里叶级数的各种类型收敛的系数而言的最佳结果。对于具有 - 系数的序列和的平滑度的 - 模，以及 Lebesgue、Lorentz、Besov 中此类和的（准）范数，获得了双边估计，和 Sobolev 空间的傅立叶系数。参考书目：99 个标题。