Meet A Class H (?) Rmander Conditions Singular Integral Operators And Their Commutators Boundedness

This thesis contains four chapters, we mainly discuss the weighted bounded-ness of singular integral operator satisfying a variant Hormander's condition, and the boundednesses of its commutators generated by the Lipschitz function and mul-tilinear commutator generated by the BMO function.In Chapter 1, we introduce the definition, notation and development of the sin-gular integral operator satisfying a variant Hormander's condition, and put forward the questions to be studied. In Chapter 2, we prove the boundedness for commuta-tor generated by the Lipschitz function with the singular integral operator satisfying a variant Hormander's condition on Lebesgue spaces and Hardy type spaces. In Chapter 3, we study the weighted weak type estimates for the multilinear commu-tator generated by the singular integral operator satisfying a variant Hormander's condition with the BMO function. In Chapter 4, We discuss the weighted (p,p) boundedness and the weighted weak (1,1) boundedness for the singular integral operator satisfying a variant LT-Hormander's condition.