8 problems

Extension conjecture. Theorem still holds for $d\geq p$.

Symmetrization conjecture. If

Albuquerque–Rezende's conjecture. There exist constants $B_{m},C_{m}>0$, depending only on $m$, such that

Simplex Calderón–Zygmund form conjecture. Then

Let $m$ be a positive integer, let $(r,p)\in(0,\infty)\times(1,\infty]$, and let $T:\ell_p^n\times\cdots\times\ell_p^n\to\mathbb{K}$ be a unimodular $m$-linear form, where $n$ is a…

Let $m,n$ be positive integers, let $pin[1, fty]$, and let $T:ellp^ntimescdotstimesellp^ntomathbb{K}$ be a unimodular $m$-linear form. The norm $|T|$ is its operator norm. **Optima…

Optimal asymptotic estimate. There exist constants $B_d,C_d<\infty$ such that

Let $k$ be a fixed positive integer. Let $y_1,\dots,y_k$ be independent vectors uniformly chosen from $\{-1,1\}^n$, let $A$ be a $k$-multilinear form whose coefficients are all non…