On boundedness of discrete multilinear singular integral operators

Let m(ξ,η)m(ξ,η) be a measurable locally bounded function defined in R2R2. Let 1⩽p1,q1,p2,q2<∞1⩽p1,q1,p2,q2<∞ such that pi=1pi=1 implies qi=∞qi=∞. Let also 00t>0. We apply this result to prove boundedness of the discrete Bilinear Hilbert transforms and other related discrete multilinear singular integrals including the endpoints.