The properties of the class of functions of generalized bounded variation are studied. The “anomaly” feature of this class is revealed. There is the notation of absolute continuity with respect to $$((p_n), \phi )$$ and it’s connection with the ordinary absolute continuity is investigated. The problems of approximation by Steklov’s functions and singular integrals are studied.

中文翻译：

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关于广义有界变分函数的类

研究了广义有界变异函数类的性质。该类的“异常”特征被揭示。$$((p_n), \phi )$$有绝对连续性的记号，研究了它与普通绝对连续性的关系。研究了Steklov函数和奇异积分的逼近问题。