The Boundedness Of The Singular Integral Operator In The Campanato Space

Based on the results of the boundedness of parameterized Marcinkiewicz integrals on weighted LP spaces,by using the estimates of classical inequal-ity and the properties of the weighted Campanato spaces,the boundedness of the parameterized Marcinkiewicz integral operators ??? with variable kernel on weighted Campanato and BMO spaces is obtained.In addition to that,based on the boundedness of Riesz transform related to higher order Schrodinger op-erators H2-1/2V and its commutator[b,H2/1/2V]on Lp spaces,where b ? BMO,by using the estimates of classical inequality and the properties of the Cam-panato spaces,the boundedness of the Riesz transform related to higher order Schrodinger operators and their commutators on Campanato and BMO spaces are obtained.