  We prove that bilinear forms associated to the rough homogeneous singular
integrals $T_\Omega$ on $\mathbb R^d$, where the angular part $\Omega \in L^q
(S^{d-1})$ has vanishing average and $1<q\leq \infty$, and to Bochner-Riesz
means at the critical index in $\mathbb R^d$ are dominated by sparse forms
involving $(1,p)$ averages. This domination is stronger than the weak-$L^1$
estimates for $T_\Omega$ and for Bochner-Riesz means, respectively due to
Seeger and Christ. Furthermore, our domination theorems entail as a corollary
new sharp quantitative $A_p$-weighted estimates for Bochner-Riesz means and for
homogeneous singular integrals with unbounded angular part, extending previous
results of Hyt\"onen-Roncal-Tapiola for $T_\Omega$. Our results follow from a
new abstract sparse domination principle which does not rely on weak endpoint
estimates for maximal truncations.
