Rough maximal bilinear singular integrals

We study the rough maximal bilinear singular integral T-Omega*(f, g)(x) = sup(epsilon>0) vertical bar integral(Rn\B(0,epsilon))integral(Rn\B(0,epsilon)) Omega((y, z)/vertical bar(y, z)vertical bar)/vertical bar(y, z)vertical bar(2n) f (x - y) g(x - z) dydz vertical bar, where Omega is a function in L-infinity(S2n-1) with vanishing integral. We prove it is bounded from L-p x L-q -> L-r, where 1 < p, q < infinity and 1/r = 1/p + 1/q. We also discuss results for Omega is an element of L-s (S2n-1), 1 < s < infinity.