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 $q\in (1,\,\infty]$.
Categories: math.CA