Parametric Marcinkiewicz Integral Estimation Under Non-double Measure

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