A sparse domination principle for rough singular integrals

We prove that bilinear forms associated to the rough homogeneous singular integrals where Ω ε Lq(Sd-1) has vanishing average and 1 < q ≤ ∞, and to Bochner-Riesz means at the critical index in Rd are dominated by sparse forms involving (1, p) averages. This domination is stronger than the weak-L1 estimates for TΩ and for Bochner-Riesz means, respectively due to Seeger and Christ. Furthermore, our domination theorems entail as a corollary new sharp quantitative Ap-weighted estimates for Bochner-Riesz means and for homogeneous singular integrals with unbounded angular part, extending previous results of Hytönen, Roncal and Tapiola for TΩ. Our results follow from a new abstract sparse domination principle which does not rely on weak endpoint estimates for maximal truncations.