带粗糙核的积分算子在齐次空间上的有界性

The Boundedness of Higher-order Commutators of Integral Operators with Rough Kernels on the Homogeneous Morrey-Herz Space

证明了一类带粗糙核的Carlderón-Zygmund奇异积分和CMO(Rn)函数生成的高阶交换子在齐次Morrey-Herz空间上的有界性;进而利用其与Marcinkiewicz积分算子的关系,得到带粗糙核的Marcinkiewicz积分高阶交换子在齐次空间Morrey-Herz上的有界性。

In this paper, the boundedness for the higher - order commutator of Carlderon - Zygmund singular integrals with rough kernel on the homogeneous Morrey -Herz space is proved, which makes it possible to get the boundeness for the higher - order commutator of a class of Marcinkiewicz integrals with rough kernel on the homogeneous Morrey -Herz space.