Criteria for Optimal Global Integrability of Hajłasz-Sobolev Functions

The author establishes some geometric criteria for a domain of ${\mathbb R}^n$ with $n\ge2$ 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 $s\in(0,\,1]$.

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