Lipschitz Estimates For Commutators Of Multi-Linear Singular Integrals Operators With Kernels Of Dini's Type

In this paper,we mainly study the boundedness of commutators that are generated by multilinear Calderon-Zygmund operators with kernels of Dini's type and Lipschitz functions.In chapter one,the history,development,signification and evolving of the theory of commutators are reviewed.In chapter two,we give a sharp maximal estimate for multilinear and iterated com-mutators that are generated by multilinear Calderon-Zygmund operators with kernels of Dini's type and Lipschitz functions.Furthermore,in the suitable index case,commutators are bounded on product of Lebesgue spaces.In chapter three,we are concerned with multilinear commutators generated by Lips?-chitz functions and multilinear Calderon-Zygmund operators with kernels of Dini's type.Furthermore,the boundedness of it on Triebel-Lizorkin spaces is obtained.In chapter four,iterated commutators generated by Lipschitz functions and multilin-ear Calderon-Zygmund operators with kernels of Dini's type are considered.Furthermore,the boundedness of it on Lipschitz spaces is obtained.