The Boundedness Of The Marcinkiewicz Integral Associated With The Schr?dinger Operator On The Weighted Function Space

Let L =-?+V be a Schr?dinger operator,where V is a nonnegative potential belonging to some reverse H?lder class.In this paper,using the estimate of the classical inequalities and the properties of the Marcinkiewicz integrals associated with Schr?dinger operators and Muckenhoupt weighted functions,together with the boundedness of clas-sical Marcinkiewicz integrals and Hardy-Littlewood maximal functions on L~p(?),we obtained the boundedness of Marcinkiewicz integrals associated with Schr?dinger oper-ators on L~p(?),where p ?[1,?).Then using the definition and atomic decomposition of weighted Hardy spacesm we established the boundedness of Marcinkiewicz integrals associated with Schr?dinger operators from H_L~1(?)to L~1(?).In the final,we discussed the boundedness of ?_j~L on weighted BMO spaces,weighted Morrey spaces.