具有粗糙核Marcinkiewicz积分交换子的Lipschitz估计

Lipschitz estimates for Marcinkiewicz integral commutators with rough kernels

Marcinkiewicz积分是分析中的一类被广泛研究的重要算子.引进一类Morrey-Herz函数空间,利用带粗糙核的Marcinkiewicz积分算子与Lipschitz函数生成的交换子在Lp空间上的有界性,证明它在更广泛的一类空间即齐次Morrey-Herz空间上的有界性.

The Marcinkiewicz integral was a class of important operators in analysis and was widely studied.A class of Morrey-Herz space was introduced.By using the fact that the commutator μΩ,b（f）（x）,which came from Marcinkiewicz integral operators with rough kernels and Lipschitz functions,had boundedness on the Lp space,a conclusion was verified that μΩ,b（f）（x） also had boundedness on the Homogeneous Morrey-Herz space.