In this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

中文翻译：

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粗糙奇异型积分算子的变指数消失Morrey型空间上的范式不等式

本文利用变量指数分析和粗糙核的性质，研究了粗糙奇异积分算子的映射性质。然后，我们显示了粗糙的Calderón–Zygmund型奇异积分算子，粗糙的Hardy–Littlewood最大算子以及有界集合上的变指数消失的广义Morrey空间中的对应交换子的有界性。实际上，以上结果是对某些已知结果的概括，基于运算符。