We find sufficient conditions which are in a sense best possible that must be satisfied by the functions of an orthonormal system in order for the Fourier coefficients of functions of bounded variation to satisfy the hypotheses of the Men’shov–Rademacher theorem. We also prove a theorem saying that every system contains a subsystem with respect to which the Fourier coefficients of functions of bounded variation satisfy those hypotheses. The results obtained complement and generalize the corresponding results in [1].

中文翻译：

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一般傅立叶系数和收敛几乎无处不在

我们找到了在某种意义上最好的充分条件，正交系统的函数必须满足这些条件，以便有界变异函数的傅立叶系数满足 Men'shov-Rademacher 定理的假设。我们还证明了一个定理，即每个系统都包含一个子系统，关于该子系统，有界变异函数的傅立叶系数满足这些假设。得到的结果对[1]中的相应结果进行了补充和推广。