Rough bilinear singular integrals

We study the rough bilinear singular integral, introduced by Coifman and Meyer [8],TΩ(f,g)(x)=p.v.∫Rn∫Rn|(y,z)|−2nΩ((y,z)/|(y,z)|)f(x−y)g(x−z)dydz, when Ω is a function in Lq(S2n−1) with vanishing integral and 2≤q≤∞. When q=∞ we obtain boundedness for TΩ from Lp1(Rn)×Lp2(Rn) to Lp(Rn) when 1