5 problems

Let $d\ge 2$, $1<p<\infty$, and let $\mathbf{R}^{(jk)}$ be the probabilistic continuous second-order Riesz transforms on $\mathbb{R}^d$. Let $p^*=\max\\{p,p/(p-1)\\}$, and let…

Weak differential subordination conjecture. There exists $C_p\geq 1$ such that, for every pair of continuous martingales $M,N:\mathbb R_+\times\Omega\to X$ with $N$ weakly differen…

Alternative-integrand conjecture. Theorem 1 of the cited work should also hold with the integrand $h_n=x_n/(\sqrt{[x]_n}\vee x_n^*)$, potentially with different constants.

Conjecture. The sharp constants satisfy $C_{p'}=C_p$, or equivalently,

Symmetry conjecture. $C_{p'}=C_p$, or equivalently,