Rough bilinear singular integrals

We study the rough bilinear singular integral, introduced by Coifman and Meyer [8], T-Omega (f, g)(x) = p.v. integral R-n integral R-n vertical bar(y, z)(-2n) Omega((y, z)/vertical bar(y, z)vertical bar)f(x - y)g(x - z)dydz, when Omega is a function in L-q(S2n-1) with vanishing integral and 2 <= q <= infinity. When q = infinity we obtain boundedness for To from L-p1 (R-n) x L-p2 (R-n) to L-p (R-n) when 1 < p1, p2 < infinity and 1/p = 1/p1 + 1/p2. For q = 2 we obtain that T Omega is bounded from L-2(R-n) x L-2(R-n) x L-1(R-n). For q between 2 and infinity we obtain the analogous boundedness on a set of indices around the point (1/2,1/2,1). To obtain our results we introduce a new bilinear technique based on tensor-type wavelet decompositions. (C) 2017 Elsevier Inc. All rights reserved.