3 problems

Szatzschneider's conjecture. Under these conditions,

Let $T\subset\ell^2$, let $B_t=\sum_i t_i\varepsilon_i$ be the canonical Bernoulli process, and let $\varphi=(\varphi_i)_{i\geqslant1}:T\to\ell^2$. Bernoulli contraction conjecture…

Let $T\subset \ell^2$ and let $X_t=\sum_{i\geqslant 1}t_i\varepsilon_i$ for $t\in T$, where the $\varepsilon_i$ are independent random signs with…