Parametric Marcinkiewicz Integral Estimation Under Non-double Measure

In the assumption that the kernel of M?(f)satisfies certain Hormander-type condi-tion,by the properties of non-doubling measures,it proves that the operator of parameter Marcinkiewicz integral M?(f)the commutators generated by parameter Marcinkiewicz integral Mb?(f)and RBMO(?)functions is bounded on the Herz-Morrey spaces for non-doubling measures.In addition,in the assumption that the kernel of M?(f)satisfies certain slightly stronger Hormander-type condition,by the properties of non-doubling measures,it proves that the multilinear commutators generated by parameter Marcinkiewicz integral (?)and Lipschitz functions is bounded on the Morrey spaces for non-doubling measures Mqp(?).The boundedness from the Morrey spaces to the Lipschitz space Lip?-n/p(?)and RBMO(?)space for non-doubling measures is obtained,respectively.