3 problems

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 $S_{\operatorname{int}}$ 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 $W$ 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…