Sharp Poincaré--Sobolev Inequalities of Choquet--Lorentz Integrals with Respect to Hausdorff Contents on Bounded John Domains

Long Huang, Yuanshou Cao, Dachun Yang +1

Let $\Omega$ be a bounded John domain in ${\mathbb{R}}^n$ with $n\ge 2$, and let ${\mathcal{H}}_{\infty }^{\delta }$ denote the Hausdorff content of dimension $\delta \in (0,n]$. In this article, the auth…