2 problems

Separated bump conjecture. Given $0<\alpha<n$ and $1<p\leq q<\infty$, the strong-type inequality for the Riesz potential holds for every pair of weights $(u,\sigma)$ satisfying the…

Let $n\geq 2$ and $0<\alpha<n$, and let $m_{\operatorname{ball}}$, $m_\mathrm{ex}$, and $m_\mathrm{crit}$ denote respectively the critical mass below which balls minimize the liqui…