Singular Integral Commutators Of A Number Of Issues

This thesis consists of three chapters, and discusses mainly the weighted esti-mates for the multilinear commutators of the 0-type Calderon-Zygmund operators and the singular integral operator which kernel function satisfying a kind of Dini conditions.In Chapter 1, we introduce the conception, significance and development of theθ-type Calderon-Zygmund operators, the singular integral operator which kernel function satisfies a kind of Dini conditions and their commutators, and put forward the question to be studied in this paper.In Chapter 2, the weighted estimates for the multilinear commutators Tb gen-eralized byθ-type Calderon-Zygmund operators and b= (b1,b2,…,bm)(bj∈OscexpL(?)j,1≤j≤m) are discussed. The weighted boundedness are established when 0< p<∞andω∈Ap, and the weighted L(logL)1/(?)-type estimates are established when p=1 andω∈A1.In Chapter 3, We study the weighted boundedness for the multilinear com-mutators of the singular integral operator when the kernel function satisfies a kind of Dini conditions. Let TΩbe the singular integral operator which kernel functionΩ∈Ls(Sn-1)(s>1) and TΩ,b the multilinear commutators generated by TΩand b= (b1,b2,…, bm), which bj∈BMO(Rn)(1≤j≤m). In the suppose ofΩsatis-fying a kind of Dini conditions, It is deduced that TΩ,b is boundedness from Lp(ω) to Lp(ω) whenω∈Ap/s', and that they satisfy corresponding weighted L(logL)m-type estimates withωs'∈A1.