Boundedness Of Singular Integral Commutators And Multilinear Littlewood-Paley Operators

In this paper we mainly discuss the boundedness of commutator and multilinear Littlewood-Paley operator on several classes of function spaces.The main contents of this paper include the following three aspects.Firstly,we discuss the necessary and sufficient conditions for the boundedness of the commutator[b,T]generated by local integrable function b and Calderon-Zygmund operator T which satisfy the non-degenerate hypothesis condition on D-regular ho-mogeneous space(LP(X),Lq(X)),where the real pairs of(p,q)satisfy 1<p,q<?.Secondly,we discuss the mapping property from LP1(Rn)x···x LPm(Rn)to Lq(Rn)of the commutator Tbj generated by local integrable function b and multilinear Calderon-Zygmund operator T which satisfy the non-degenerate hypothesis condition.This result extends some results of Hytonen' s in Reference[1].Finally,based on the boundedness result of the general Littlewood-Paley operator g? on classical Lebesgue space Lp(Rn)and using the method of function decomposi-tion,we obtain the boundedness of multilinear Littlewood-Paley operator on Lebesgue space and Herz-Morrey space with variable exponent.