Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals

Let r > 4 3 and let Ω ∈ L r ( S 2 n - 1 ) have vanishing integral. We show that the bilinear rough singular integral T Ω ( f , g ) ( x ) = p.v. ∫ R n ∫ R n Ω ( ( y , z ) / | ( y , z ) | ) | ( y , z ) | 2 n f ( x - y ) g ( x - z ) d y d z , satisfies a sparse bound by ( p , p , p )-averages, where p is bigger than a certain number explicitly related to r and n . As a consequence we deduce certain quantitative weighted estimates for bilinear homogeneous singular integrals associated with rough homogeneous kernels.