Abstract
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 Lp × Lq → Lr, 1<p,q<infty and r>frac {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.
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