Cruz-Uribe–Pérez two-weight conjecture for Calderón–Zygmund operators

Let $1<p<\frac{\infty}{ }$, let $A$ and $B$ be Young functions, and let $\bar A$ and $\bar B$ denote their complementary Young functions. For a cube $Q$, write $\|\cdot\|_{A,Q}$ and $\|\cdot\|_{B,Q}$ for the corresponding localized Luxemburg norms. Let $u$ and $v$ be weights, and let $T$ be a Calderón–Zygmund operator. Cruz-Uribe–Pérez two-weight conjecture. If

$$\bar A\in B_{p'},\qquad \bar B\in B_p,$$

and

$$\sup_Q\|u^{1/p}\|_{A,Q}\|v^{-1/p}\|_{B,Q}<\infty,$$

then

$$\|Tf\|_{L^p(u)}\le c\|f\|_{L^p(v)}.$$

This conjecture was proved under certain restrictions on $A$ and $B$; the statement in the displayed generality is therefore recorded as solved in the source's account.