We introduce a class of tri-linear operators that combine features of the bilinear Hilbert transform and paraproduct. For two instances of these operators, we prove boundedness property in a large range D = {(p 1 , p 2 , p 3 ) ∈ R 3 : 1 < p 1 , p 2 < ∞, p 1 1 + p 1 2 < 32 , 1 < p 3 < ∞}.

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