Two-weight bounds for sparse square functions, uniform over sparse families, do not imply two-weight bounds for the Hilbert transform.
Lacey, On the separated bumps conjecture for Calder´ on–Zygmund operators, Hokkaido Math
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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.