4 problems

A Schauder-Orlicz decomposition is a Schauder decomposition whose associated coefficient space is an Orlicz sequence space. Fix the dimensions of its component subspaces. Uniquenes…

Uniqueness conjecture. If there is a unique (up to equivalence near $0$) mean zero function $f$ whose independent copies are equivalent in $L_p$ to the unit vector basis in $l_M$,…

The crossed-product factorization conjecture. For any Orlicz function $\psi$,

Let $H_0^1({\mathbb D})$ be the Sobolev space on the unit disk, let $\eta_\zeta$ denote the disk automorphism associated with $\zeta\in{\mathbb D}$, and let $h_s$ be the radial dil…