Marcinkiewicz Integral With Rough Kernel And Schrödinger Operator

In this paper,we introduced the definition of Marcinkiewicz integral associated with Schr?dinger operator and Marcinkiewicz integral with rough kernel associated with Schr?dinger operator.We do this by using the classical inequalities and properties of Muckenhoupt weighted functions,together with the properties of rough kernel and Riesz kernel,and on the basis of the boundedness of Marcinkiewicz integral with rough kernel associated with Schr?dinger operator and its commutators on Lebesgue spaces and on weighted Lebesgue spaces to established the boundedness of Marcinkiewicz integral with rough kernel associated with Schr?dinger operator and its commutators on weighted Morrey spaces associated with Schr?dinger operator and on weighted Morrey spaces with variable exponent related to the nonnegative potential.