Resumen de Two weight inequalities for bilinear forms

Kangwei Li

• Let 1≤?0

  When ??=|?| and ?=? , Bernicot, Frey and Petermichl showed that B(f, g) dominates ⟨??,?⟩ for a large class of singular non-kernel operators. We give a characterization for the above inequality and then obtain the mixed ??−?∞ estimates and the corresponding entropy bounds when ??=|?| and ?=? . We also propose a new conjecture which implies both the one supremum conjecture and the separated bump conjecture.