Compact Commutators of Rough Singular Integral Operators. Issue 1 (1st March 2015) - Chen, Jiecheng; Hu, Guoen
Abstract: Let b BMO( R^n ) and T_Ω 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, using Fourier transform estimates and approximation to the operator T_Ω by integral operators with smooth kernels, it is proved that if b CMO( R^n ) and Ω satisfies certain minimal size condition, then the commutator generated by b and T_Ω is a compact operator on L^p( R^n ) for appropriate index p . The associated maximal operator is also considered.