Sparse bounds for maximal rough singular integrals

Let $Ω\in L^1(S^{d-1})$ have vanishing average, and let $T_Ω^\ast$ be the maximal truncation of the associated rough homogeneous singular integral. We prove quantitative sparse bounds for $T_Ω^\ast$. If $Ω\in L^\infty(S^{d-1})$, then, for every $1<p<\infty$, \[ \|T_Ω^\ast\|_{(1,p)\text{-}\mathrm{s