Boundedness Of The Commutators Of Littlewood-Paley Operators

The research of Littlewood-Paley operator and its related problems is one of the important topics in Harmonic Analysis.This paper gives the boundedness of the commutators of Littlewood-Paley operators on some spaces.In chapter one,similar to the study of Littlewood-Paley operator,we discuss the boundedness properties of commutator of Littlewood-Paley operator on weighted Herz-Hardy space,from weighted Herz-Hardy space H(?)_q^α,p(ω₁,ω₂)to weighted Herz space(?)_q^α,p(ω₁,ω₂)and from weighted Herz-Hardy space H(?)_q^α,p(ω₁,ω₂)to weighted weak Herz space W(?)_q^α,p(ω₁,ω₂).In 2006,Wu Changhong and Liu Lanzhe gave the boundedness properties of multilinear commutator of Littlewood-Paley operator.Motivated by this,in chapter two,we obtain the boundedness properties of multilinear commutators of Littlewood-Paley operators on Herz-Hardy space.In chapter three,we introduce Herz-Morrey space,which is related to Herz space, and we also give the boundedness properties of Marcinkiewicz integral operator on this space.Furthermore,in chapter four,we consider weighted Herz-Morrey space of ho-mogeneous type,and the boundedness properties of some sublinear operators are established on this space.