Resumen de Weighted estimates for maximal bilinear rough singular integrals via sparse dominations

Zhian Wang, Qingying Xue, Xinchen Duan

• Let x=(x_1,x_2) with x_1,x_2 \in \mathbb {R}^n and let K(x)={\Omega \big ({x}/{|x|}\big )}{\big |x\big |^{-2n}}, where \Omega \in L^{\infty }(\mathbb {S}^{2n-1}) and satisfies \int _{\mathbb {S}^{2n-1}}\Omega =0. We show that the maximal truncated bilinear singular integrals with rough kernel K(x_1,x_2) satisfy a sparse bound by (p, p, p)-averages for all p>1. As consequences, we obtain some quantitative weighted estimates for these rough singular integrals. A pointwise sparse domination for commutators of bilinear rough singular integrals were also established, which can be used to establish some weighted inqualities.