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

Zhian Wang, Qingying Xue, Xinchen Duan

• Let x=(x1,x2) with x1,x2∈Rn and let K(x)=Ω(x/|x|)∣∣x∣∣−2n, where Ω∈L∞(S2n−1) and satisfies ∫S2n−1Ω=0. We show that the maximal truncated bilinear singular integrals with rough kernel K(x1,x2) 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.