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).
基金
supported by National Natural Science Foundation of China(Grant No.11371370)
