7 problems

The non-resonant boundedness conjecture. Up to end-points, both operators have the boundedness range

Let $\alpha$ and $\beta$ be non-zero positive real numbers, and let $T^{\alpha,\beta}$ be the trilinear operator defined using smooth cutoff functions $\widehat{\Phi_1}$ and…

Unified weighted-condition conjecture. There is a constant $C$ such that

Cruz-Uribe–Martell–Pérez conjecture. The conclusion of the preceding mixed weighted theorem should remain valid under a weaker and more general hypothesis than the assumptions stat…

Multilinear Marcinkiewicz integral extrapolation conjecture. If $\mu$ is bounded from $L^{q_1}({\mathbb R}^n)\times\cdots\times L^{q_m}({\mathbb R}^n)$ to $L^q({\mathbb R}^n)$ for…

Let $\mathcal{L}$ denote the multi-ideal of all continuous multilinear operators, let $\mathcal{CC}$ denote the multi-ideal of completely continuous linear operators, and let…

Bernardino's optimality conjecture. The value $\frac{2}{m+1}$ is optimal; equivalently, the universal assertion fails for every $g_m<\frac{2}{m+1}$.