Estimation Of Several Kinds Of Integral Operators On ?-central Morrey Spaces

In this dissertation,we mainly research the weighted estimations of the Marcinki-ewicz integrals and their commutators,the strong singular integrals and their com-mutators and the singular integrals with the variable Calderon-Zygmund kernel and their commutators on ?-center Morrey spaces.The main results are stated as follows.Firstly,by using the method of function decomposition,the properties of A(p,q)weight and the tools of Holder's inequality,the weighted estimations of Marcinkiewicz integrals and their commutators on Lebesgue spaces are obtained.Secondly,through the weighted estimations of the commutators generated by the strong singular integrals and the BMO function on the Lebesgue spaces,we obtain the weighted estimations of the integrals and their commutators on ?-center Morrey spaces.Finally,through the weighted estimations of the commutators generated by the singular integrals with the Calderon-Zygmund kernel and their commutators on Lebesgue spaces,the weighted estimations of the integrals and their commutators on the ?-center Morrey spaces are obtained.