Criteria for Optimal Global Integrability of Hajłasz-Sobolev Functions

Abstract

The author establishes some geometric criteria for a domain of ${\mathbb{R}}^n$ with $n\ge 2$ to support a $(pn/(n-ps),p{)}_s$-Hajłasz-Sobolev-Poincaré imbedding with $s\in (0,1]$ and $p\in (n/(n+s),n/s)$ or an $s$-Hajłasz-Trudinger imbedding with $s\in (0,1]$.

arXiv commentto appear in Illinois J. Math