The composition of singular integral operators with nonsmooth kernels

Let $T_1$, $T_2$ be two singular integral operators with nonsmooth kernels introduced by Duong and McIntosh. In this paper, by establishing certain bi-sublinear sparse domination, the authors obtain some quantitative bounds on $L^p({\mathbb{R}}^n,w)$ with $p\in (1,\mathrm{\infty })$ and $w\in A_p({\mathbb{R}}^n)$ for the composite operator $T_1{T}_2$. Some weighted weak type endpoint estimates are also given.