3 problems

Let $\alpha\geq -1/2$, $p\in(1,\infty)$, and let $w\colon\mathbb{R}\to[0,\infty)$ satisfy … where the supremum is over all intervals $B\subset\mathbb{R}$ and $1/p+1/p'=1$. The weig…

Spherical-function growth conjecture. If $\lambda,X\in\overline{\mathfrak{a}^+}$, then

Potential-kernel conjecture. For $x\in B^+$ and $y\in S^+$,