3 problems

Let $p$ and $q$ satisfy $p\le 2\le q$, and let $A=(a_{ij})_{i\le m,j\le n}$ be a deterministic $m\times n$ matrix. Write $p^*$ for the Hölder conjugate of $p$, and let…

The UMD$^-_{\rm PW}$ conjecture. If $\Phi\in\Delta_2$, then $L^{\Phi}(T)$ is UMD$^-_{\rm PW}$.

Let $\mathbb H$ be the discrete Heisenberg group, let $B_n$ be its radius-$n$ ball with the word metric $d_W$, and let $c_1(B_n,d_W)$ denote the least distortion of an embedding of…