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

arxiv: 1511.06465 · v2 · pith:WQVS4F2Fnew · submitted 2015-11-20 · 🧮 math.FA

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

Xiaodan Zhou This is my paper

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keywords ahlforscontinuousfunctionsmetricregularspaceuniformlywhen

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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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