2 problems

Let $d\ge 2$. Let $\mathcal D^d$ be the dyadic rectangles in $[0,1)^d$, and let $h_R$ be the associated multiparameter Haar function. For each $n\in\mathbb N_0$, consider rectangle…

Small ball inequality conjecture. For every $d\ge3$, the displayed inequality should hold. It is a central conjecture in the paper, with consequences for irregularities of distribu…