Research On The Commutators Of Multilinear Marcinkiewicz Operators On Non-homogeneous Metric Measure Spaces

As is well-known,Marcinkiewicz integral operators and their commutators play an important role in harmonic analysis.A series of Marcinkiewicz type integral operators and their commutators are derived from Marcinkiewicz integral operators.In this thesis,we will further study the boundedness of parametric Marcinkiewicz operators and their commutators on non-homogeneous metric measure space.This paper consists of five chapters.The first chapter is the introduction,it mainly introduces the research status of the boundedness for some Marcinkiewicz integral operators and their commutators in different spaces.In the second chapter,it mainly introduces the basic concepts and related theorems of parametric Marcinkiewicz integral operators and their commutators.The third chapter proves the boundedness of m-order commutators Mb,m?(f)generated by the Log-Dini type parametric Marcinkiewicz integral operators with RBMO functions b over Lebesgue space with non-homogeneous metric measure space.The forth chapter,we further establish the commutators of multilinear commutators(?)and prove the boundedness under the same conditions.The fifth chapter is the summary and prospect of this paper,pointing out the expansion direction of parameter type Marcinkiewicz integral operators and their commutators.