The Boundedness For Commutators Of Marcinkiewicz Integral And Multilinear Square Operators

In this dissertation,we discuss the boundedness for commutators of Marcinkiewicz integral and multilinear square operator.The main framework of this dissertation is as the following.The first chapter,we introduce the dynamic of the development and the main results that made by chinese and foreign scholars of harmonic analysis.And the same time,we introduce the reason why we choose this topics and the significance and conclusion of this dissertation.The second chapter,we present the boundness for commutator of Marcinkiewicz integral on weighted Lebesgue space,weighted Herz space and weighted weak Herz space.The third chapter,we present the boundness for iterative commutator TΠb and m-linear commutator T∑b of miltilinear square operator on product weighted Lebesgue space.