The Boundedness Of Marcinkiewicz Integral Operator Related To Generalized Schr(?)dinger Operator

In this thesis,we introduced the definitions and basic properties of the variable expo-nent Lebesgue space,and the Marcinkiewicz integral operator associated with generalized Schr(?)dinger operators and its commutators.We showed that the Marcinkiewicz integral operator associated with generalized Schr(?)dinger operator is bounded on BMOL,and from HL1(Rn)to L1(Rn).Then,using the classical inequalities,by the properties of the vari-able exponents and the auxiliary functions,and the basic properties of the Marcinkiewicz integral operator associated with generalized Schr(?)dinger operator and the commutators generated by the Marcinkiewicz integral operator and BMO function,we showed that the Marcinkiewicz integral operator associated with generalized Schr(?)dinger operator and its commutators are bounded on Herz-Morrey spaces with variable exponents.