10 problems

Stein's square function conjecture. For $p>2$, the estimate

Let $U_{1},U_{2},U_{3}\subset U$ be a $\nu$-disjoint triple of squares, meaning that each has side length comparable to $\nu$ and distinct squares are separated by at least $\nu$.…

Let $\Omega$ be a collection of pairwise disjoint intervals, let $T^{\Omega}_{\operatorname{RF}}$ be the Rubio de Francia square function associated with the Fourier restrictions t…

Let $S_{\operatorname{int}}$ be the intrinsic square function and let $w\in A_2$ be a Muckenhoupt weight, with characteristics $[w]_{A_2}$ and $[w]_{A_{\infty}}$. The weighted weak…

Let $0<\delta<1$, $\kappa>\frac{10}{\delta}$, and $q>3$. In $\mathbb{R}^{3}$, let the square function inequality $(\mathrm{prob\ ext\ square})$ be the inequality defined earlier in…

The square-function conjecture. For every $\alpha>\alpha(p)-\frac12$, there is a constant $C$ such that

Square-function estimate conjecture. For every $\epsilon>0$, there exists $C=C(\epsilon)$ such that

Let $d\ge 2$ and define the Bochner–Riesz square function by … where $\mathcal R_t^\alpha$ is the Bochner–Riesz operator. Square-function conjecture. For $p>2$, the operator…

Let $W$ be a $d\times d$ matrix weight in $A_2$, and let $S_W$ denote the associated square function on $L^2(W)$. Matrix weighted square function conjecture. … The scalar analogue…

Let $1<p<\infty$ and let $A_p$ denote the Muckenhoupt characteristic of a weight. Consider the Littlewood–Paley square function associated with a weight in $A_p$. Lerner's conjectu…