Off-Diagonal Estimates for Bilinear Commutators

We find a minimal notion of non-degeneracy for bilinear singular integral operators T and identify testing conditions on the multiplying function b that characterize the L-p x L-q -> L-r, 1 < p, q < infinity and r > 1/2, boundedness of the bilinear commutator [b, T](1 )(f, g) = bT (f, g) - T (bf, g). Our arguments cover almost all arrangements of the integrability exponents p, q, r with a single open problem presented in the end. Additionally, the arguments extend to the multilinear setting.