The Boundedness Of Multilinear Commutators Of Singular Integral Operators And Fractional Integral Operators Related To Smooth Functions

In this paper, we study the boundedness of multilinear commutators of singular integral operators and fractional integral operators with smooth functions. This paper is organized as following.In chapter 1, we simply introduce the development in the study of the boundedness of multilinear commutators of singular integral operators and fractional integral operators.In chapter 2, we study the boundedness of commutators of singular integral operators and fractional integral operators related to Besov functions from Ld(Rn) to Lr(Rn). In this chapter, we prove that the operators [6,T]m and [6,Il}m are bounded from Ld(Rn) to Lr(Kn).In chapter 3, we investigate the boundedness of multilinear commutators of singular integral operators and fractional integral operators with Lipschitz functions on the Hardy-type spaces. In this chapter, we obtain the mapping properties of [b,T] and [b,Il,] on the Lp(Rn), Hardy type spaces H(Rn) and Herz-Hardy type spaces HK (Rn).In chapter 4, we discuss the boundedness of the multilinear commutators generated by singular integral operators and fractional integral operators with Lipschitz functions. In this chapter, we show that the commutators [b, T] are bounded from Lp(Rn) to F(Rn), as well as [b,Ia] from Lp(Rn) to F(Rn).