Within the framework of variable-exponent Morrey and Morrey–Herz spaces, we prove some boundedness results for the commutator of Marcinkiewicz integrals with rough kernels. The proposed approach is based on the theory of variable exponents and on the generalization of the BMO-norms.

中文翻译：

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可变Morrey型空间中具有粗糙核的Marcinkiewicz积分的交换子。

在指数可变的Morrey和Morrey-Herz空间的框架内，我们证明了具有粗糙核的Marcinkiewicz积分交换子的一些有界结果。所提出的方法基于变量指数理论和BMO范数的推广。