16 problems

Dubois-Violette's conjecture. Any $3$-regular multilinear form provides an algebra in $\mathcal{C}_2$.

Sharp-exponent conjecture. For a range of $1<p_1,\ldots,p_k<\infty$, this estimate holds, and in each case the exponent of $\lambda$ is sharp. The proposed exponent depends only on…

Concave multilinearization inequality. Then

Bohnenblust–Hille constant conjecture. The value of the $\mathrm{BH}$ constant for $d$-linear tensors is conjectured to be

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…

For each $m\in\mathbb{N}$, let $C_m$ denote the optimal constant in the $m$-linear Bohnenblust–Hille inequality over the real scalars. Pellegrino–Teixeira conjecture. The optimal c…

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

For an $m$-linear form $T$ on $c_0$, let $B_m$ denote the optimal constant in the classical Bohnenblust–Hille inequality. Universality Conjecture. The optimal constants $B_m$ are b…

Multilinear determinantal singular integral conjecture. If $n-1<p_j<\infty$ for $j=1,\ldots,n$ and $\sum_{j=1}^n 1/p_j=1$, then

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…

Let $w$ be a 3-regular $(N+1)$-linear form on $mathbb K^g$, with $N\geq 2$ and $g\geq 2$, and let ${\mathcal A}(w,N)$ denote the associated graded algebra. Van den Bergh's converse…