Two-weight bounds for sparse square functions, uniform over sparse families, do not imply two-weight bounds for the Hilbert transform.
Cruz-Uribe, Alexander Reznikov, and Alexander Volberg , Logarithmic bump conditions and the two-weight boundedness of Calder´ on–Zygmund operato rs, Adv
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Two-weight estimates for sparse square functions and the separated bump conjecture
Two-weight bounds for sparse square functions, uniform over sparse families, do not imply two-weight bounds for the Hilbert transform.