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Mathematics  2015 

Sobolev functions in the critical case are uniformly continuous in $s$-Ahlfors regular metric spaces when $s \le 1$

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Abstract:

We prove that functions in the Haj\l{}asz-Sobolev space $M^{1,s}$ on an $s$-Ahlfors regular metric space are uniformly continuous when $s\le 1$.

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