3 problems

Let $T$ be a sparse operator, let $1<p<q<\infty$, and let $\mathcal{D}_{p,p}$ and $\mathcal{D}^{\ast}_{p,p}$ denote the corresponding direct comparison bump quantities for the case…

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 $\mathbb{R}^d$,