10 problems

Bilinear sparse square-function domination conjecture. There exist $\eta=\eta(d,T)\in(0,1)$ and an $\eta$-sparse family $\mathcal{S}$ of cubes in $\mathbb{R}^d$, depending on…

Sparse square-function criterion. Suppose that for every $0<\eta<1$ and every $\eta$-sparse family $\mathcal{S}$ of cubes in $\mathbb{R}^d$,

Let $1<p<q$, let $w\in C_q$, let $T$ be a Calderón--Zygmund operator, and let $f\in C_c^\infty(\mathbb{R}^n)$. Linear quantitative CFI conjecture. The estimate … should hold. The p…

Let $T$ be a one-sided Calderón–Zygmund operator: an operator bounded on $L^2$ with a kernel $K(x,y)$ satisfying … … for fixed $0<\alpha\leq 1$, and $K(x,y)=0$ when $x<y$. For…

Hytönen–Lacey one-supremum conjecture. The estimate

Let $1<p<\infty$, let $p'=p/(p-1)$, let $u$ and $v$ be weights, and let $T$ be a Calderón–Zygmund operator. Write $M:L^p(u)\to L^p(v)$ for boundedness of the maximal operator betwe…

Separated bumps conjecture. For all Calderón-Zygmund operators $T$, there holds

Let $1<p<finfty$, let $T$ be a Calderon-Zygmund operator, and let $w otin Ap$. Write $p'=p/(p-1)$ and let $\sigma=w^{-1/(p-1)}$ be the dual weight. For mixed constants,…

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 $\|\cdot\|_{A,Q}$ an…

Sharp $A_p$–$A_\infty$ conjecture. There is a constant $C_{T,p}$ such that