Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of an analogue of Hardy-Littlewood test and its consequences, which were earlier obtained in the case of bounded sequence {p_k} defining the system, are proved.

中文翻译：

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在无界pk情况下Vilenkin系统上Fourier级数的Hardy-Littlewood检验的类比

考虑关于零维紧凑交换群的字符系统的级数。证明了Hardy-Littlewood检验类似物的一般化及其后果，这些后果是在定义系统的有界序列{ p _k }的情况下较早获得的。