Lp(Rn) boundedness for the commutator of a homogeneous singular integral operator

The commutator of a singular integral operator with homogeneous kernel ${\mit \Omega }(x)/|x|^n$ is studied, where ${\mit \Omega }$ is homogeneous of degree zero and has mean value zero on the unit sphere. It is proved that ${\mit \Omega }\in L(\mathop {\