6 problems

Hörmander's conjecture. If $\phi$ satisfies (H1) and (H2), then

Let $n\ge 3$, let $\mathcal{E}$ be the class of all complex elliptic operators under study, and for $L\in\mathcal{E}$ let $p_-(L)$ be the lower endpoint of the maximal interval of…

Strong spherical maximal function conjecture. For all $n\geq 2$ and $p>\frac{n+1}{n-1}$, there exists a constant $C_{n,p}>0$ such that

Interior $L^p$ estimate conjecture. One should have

Let $0<\alpha<2$, let $\Omega\subset\mathbb{R}$ be a bounded domain, and let $e_\lambda$ be an eigenfunction of the fractional Laplacian on $\Omega$ with eigenvalue parameter…

A multi-index $\vec{\alpha} \in \mathbb{R}^n$ is called semi-degenerate when it satisfies the semi-degeneracy conditions defined in the paper, and $C^{\vec{\alpha}}$ denotes the co…