5 problems

Stein's conjecture. For every $p\in(1,\infty]$ there is a constant $C_p>0$ such that

Let $G\subseteq\mathbb{R}^n$ be a centrally symmetric convex body. For $p\in(1,\infty]$, let $C_p(n,G)$ denote the best constant such that … where $\mathbf M_t^G$ is the integral H…

For $d>1$, let $\mathbb{K}_{\mathbb{H}^{(k)}}$ denote the probabilistic continuous Riesz transform in the $k$th coordinate, acting on $L^p(\mathbb{R}^d)$, where $1<p<\infty$ and…

Let $d\in\mathbb{N}$ and let $B^q(d)\subset\mathbb{R}^d$ be a $q$-ball. The discrete restricted maximal function is denoted by $\mathcal{M}_{\ast,>D}^{G}$, and $\mathcal{C}(G,p)$ d…

Dimension-free maximal inequality conjecture. The inequality holds for all $p\in(1,\infty]$ and all convex symmetric bodies $G\subset\mathbb{R}^d$, with $C_p(d,G)$ independent of…