Compactness Of Commutators Of Several Kinds Of Integrals

In this dissertation,we mainly study the compactness of some singular integral commutators on some classical function spaces.The main results are as follows.In section 1,we mainly introduces the research background and basic concepts of this paper.In section 2.by applying the properties of the sphere harmonic,we prove that the commutator of the variable kernel singular integral[b,T]is compactness operator on Morrey space Lp,?(Rn).Furthermore,under a certain condition,there exists p satisfying 1<p<?,such that the commutator[b,T]is compactness operator on Morrey space Lp,?(Rn),we can obtain b ? VMO(Rn).In section 3,with the tool of the estimate of the Fourier transform,Littlewood-Paley theory and the approximations of the identity,and so on,we prove that the commutator of the Marcinkiwicz integral of the homogeneous kernel is a compact operator on Lp(Rn)under a certain condition.