带变量核的MarcinkiewiczMorrey-Herz算子及其交换子在加权空间上的有界性

摘要

证明了一类带变量核的Mareinkiewicz积分算子μΩ及其与BMO函数生成的交换子μb/Ω在加权Lp空间上的有界性，并在此条件下证明了带变量核的μΩ及μb/Ω在加权Morrey-Herz空间上的有界性，这些结果是一些已知定理的推广．%In this paper, the weighted Lp boundedness of Marcinkiewicz integral operators with variable kernels μΩ and their commutators with BMO functions areμb/Ω analyzed;under the same conditions, the boundedness ofμΩ and μb/Ω on weighted Morrey-Herz spaces are obtained. These results are the generalizations of some known theorems for classical Marcinkiewicz integral operators.