Weighted Norm Inequalities for Maximal Multi-sublinear Rough Singular Integrals

We continue our study of multilinear rough homogeneous singular integrals by establishing weighted estimates for their maximal truncations. Let $m\ge2$ and let $Ω\in L^q(\mathbb{S}^{mn-1})$, $1<q\le\infty$, have mean zero. For $1<p_1,\dots,p_m<\infty$ with $p_j\ge q'$ and $1/p=\sum_{j=1}^m1/p_j$, we