Endpoint Estimates For Commutators Of Singular Integral Operators

In this paper, we mainly study the boundedness for commutators of differenttype kernels singular integral operators on Lp(Rn) and Hardy type spaces. The whole paper is divided into three chapters. In the first chapter, we are mainly devoted to singular integral operator, com-mutator generated by singular integral operator with a function in BMO and some basic concepts, then overview the celebrated results and relative conclusions. In the second chapter, we study higher order maximal commutators Tb,m* gen-erated by Calderon-Zygmund singular integral operator and a function in BMO.In virtue of the estimation of the Sharp maximal function, we obtain that they satisfy L(log L)m type inequality and are bounded on Lp(Rn) (1<p<∞). In the third chapter, we change condition: into stronger condition: obtaining commutator of Lq-Dini (1<q<∞) type kernel singular integral op-erator [b,T] satisfies L(log L) type inequality. Meanwhile, we also get estimate for [b, T] on Hardy type spaces.