Weighted Norm Inequalities Of Marcinkiewicz Integrals Operator And Its Commutators

In this paper,we study the boundedness of Marcinkiewicz integral and its commutators.The contents are organized as follows.In chapter 1.we introduce the background of Marcinkiewicz integral and academic achieve-ments of relevant scholars at home and abroad.In chapter 2,we study the(H1,L1),(L?,BMO)and(LP,LP)type boundedness for the Marcinkiewicz integral.In chapter 3,we consider weighted norm inequalities of commutators generalized by Marcinkiewicz integrals with the weighted Lipschitz functions on weighted Hardy spaces and weighted Herz type Hardy spaces.