Some Problems On Commutators Generated By Singular Integral Operators And Oscillatory Integral Operators

In this paper, we study the boundedness of the commutators generated by singular integral operators whose kernel are rough with Lipschitz functions. Also, we study the boundedness of the commutators generated by oscillatory integral operators whose kernel are rough with Lipschitz function. This paper is organized as follows.In Chapter 1, we simply introduce the development in the study of the boundedness of some singular integral operators, oscillatory integral operators with rough kernel and the related commutators.In Chapter 2, whenΩ∈Ls(Sn-1)(s>n-α/n), we study the boundedness of the commutators generated by singular integral operators with Lipschitz function from L1 (Rn) to weak Ln( n)L ?αR and from Lq ( Rn) to L p ( Rn),whereIn Chapter 3, when ( ( ))?∈Ln ?nαLogLSn?1, we study the boundedness of commutators generated by singular integral operators with Lipschitz function fromIn Chapter 4, we study the boundedness of the commutators generated by oscillatory integral operators whose kernel are rough with Lipschitz function.