Compactness of the commutators of homogeneous singular integral operators  

作　　者：GUO XiaoLi HU GuoEn 

机构地区：[1]College of Mathematics and Information Science,Zhengzhou University of Light Industry [2]Department of Applied Mathematics,Zhengzhou Information Science and Technology Institute

出　　处：《Science China Mathematics》2015年第11期2347-2362,共16页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11371370)

摘　　要：Let TΩ be the singular integral operator with kernel Ω（x）/｜x｜n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈（lnL）2 （Sn- 1）, then the commutator generated by TΩ and CMO（Rn） function, and the corresponding discrete maximal operator, are compact on LP（Rn, ｜s｜γp） for p∈ （1, ∞） and γp ∈ （-1, p-l）Let TΩ be the singular integral operator with kernel Ω(x)/|x|~n,where Ω is homogeneous of degree zero,integrable and has mean value zero on the unit sphere S^(n-1).In this paper,by Fourier transform estimates,Littlewood-Paley theory and approximation,the authors prove that if Ω∈L(lnL)~2(S^(n-1)),then the commutator generated by T_Ω and CMO(R^n) function,and the corresponding discrete maximal operator,are compact on L^p(R^n,|x|^(γp)) for p∈(1,∞) and γ_p ∈(-1,p-1).

关 键 词：COMMUTATOR homogeneous singular integral operator compact operator maximal operator 

分 类 号：O177[理学—数学]