A sparse domination principle for rough singular integrals

We prove that bilinear forms associated to the rough homogeneous singular integrals ¶ TΩf(x) = p.v.∫ ℝdf(x − y)Ω( y |y|) ỵ |y|d, ¶ where [math] has vanishing average and [math] , and to Bochner–Riesz means at the critical index in [math] are dominated by sparse forms involving [math] averages. This domination is stronger than the weak- [math] estimates for [math] and for Bochner–Riesz means, respectively due to Seeger and Christ. Furthermore, our domination theorems entail as a corollary new sharp quantitative [math] -weighted estimates for Bochner–Riesz means and for homogeneous singular integrals with unbounded angular part, extending previous results of Hytönen, Roncal and Tapiola for [math] . Our results follow from a new abstract sparse domination principle which does not rely on weak endpoint estimates for maximal truncations.