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We continue the investigation initiated in [Grafakos, L. and Li, X.: Uniform bounds for the bilinear Hilbert transforms (I). Ann. of Math. (2)
159 (2004), 889-933] of uniform Lp bounds for the family of bilinear Hilbert transforms
Hα,β(f,g)(x) = p.v. ∫R f(x - αt) g (x - βt) dt/t.
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