  Let $\Omega$ be homogeneous of degree zero and have mean value zero on the
unit sphere ${S}^{d-1}$, $T_{\Omega}$ be the homogeneous singular integral
operator with kernel $\frac{\Omega(x)}{|x|^d}$ and $T_{\Omega,\,b}$ be the
commutator of $T_{\Omega}$ with symbol $b$. In this paper, we prove that if
$\Omega\in L(\log L)^2(S^{d-1})$, then for $b\in {\rm BMO}(\mathbb{R}^d)$,
$T_{\Omega,\,b}$ satisfies an endpoint estimate of $L\log L$ type.

Classical Analysis and ODEs