Endpoint Estimates For Commutators

In this thesis,the author studies the endpoint estimate for some commutators.This thesis consists three chapters.Chapter 1 presents the background and give out some necessary notations as well as definitions of spaces.In chapter 2,the boundedness of the commutator generated by strongly singular Calderon - Zygmund operator and Lipschitz function is discussed on the weighted L~p space and weighted Hardy-type space.In chapter 3,we consider the endpoint estimates for the commutator generated by Littlewood-Paley and LMO function and it's weighted endpoint estimates.