3 problems

Density-basis differentiation conjecture. If $M_{\mathcal{B}}f(x)<\infty$ almost everywhere, then

Let $B$ be a homothecy invariant density basis on $\mathbb{R}^n$, and let $\varphi_B$ be its halo function, defined by $\varphi_B(t)=1$ for $0\leq t\leq 1$ and … for $t>1$, where t…

Exact-level-set criterion. Then there exist a set $E_\gamma$ and a constant $c(\gamma)>1$ such that