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 $\hat{I}\text{c◯}$ be a bounded John domain in ${\mathbb{R}}^n$ with $n\ge 2$, and let ${\mathcal{H}}_{\infty }^{\hat{I}}´$ denote the Hausdorff content of dimension $\hat{I}´\in (0,n]$. In this article, the a…