Parameter Marcinkiewicz Integrals Commutators On Non-homogeneous Metric Measure Spaces

In this dissertation,we shall mainly study the Marcinkiewicz integral and com-mutator on the nonhomogeneous metric measure spaces.The main results are as follows.In Section 1,under the some conditions about the kernel,it is proved that the commutator Mbs???generated by the parameter Marcinkiewicz integral M^s???and Lip_????function b is not only bounded from the Hardy space H¹???to the Lebesgue space L^1/?1-?????,but also bounded from the Lebesgue space L^????to the RBMO???space.In Section 2,we obtain the boundness of parameter Marcinkiewicz integral com-mutator M_b^s???on the Morrey space M_q^p???.And we proved M_b^s???is bounded from M_q^1/????to RBMO???.