  Let $\Omega$ be homogeneous of degree zero and have mean value zero on the
unit sphere ${S}^{n-1}$, $T_{\Omega}$ be the convolution singular integral
operator with kernel $\frac{\Omega(x)}{|x|^n}$. For $b\in{\rm
BMO}(\mathbb{R}^n)$, let $T_{\Omega,\,b}$ be the commutator of $T_{\Omega}$. In
this paper, by establishing suitable sparse dominations, the authors establish
some weak type endpoint estimates of $L\log L$ type for $T_{\Omega,\,b}$ when
$\Omega\in L^q(S^{n-1})$ for some $q\in (1,\,\infty]$.
