Commutators Generated By Singular Integrals And Lipschitz Functions

This dissertation is devoted to the boundedness of commutators generated by singular integrals and Lipschitz functions. A series of new results are obtained. These results improve or extend the results in the literatures. The dissertation is organized as the following:In Chapter 1, there are the background, the recent development of commutators generated by singular integrals and main results of the dissertation.In Chapter 2, the boundedness of multilinear commutators of singular integral operators whose kernels are variable with mixed homogeneity in Lebesgue spaces is obtained.In Chapter 3, the boundedness of commutators of multilinear singular integrals with Lipschitz functions in product Lebesgue spaces is obtained.In Chapter 4, the boundedness of commutators generated by multilinear singular integrals and Lipschitz functions from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces is obtained.