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

Zhou, Xiaodan

doi:10.1090/proc/13220

Sobolev functions in the critical case are uniformly continuous in $s$-Ahlfors regular metric spaces when $s\le 1$
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Proc. Amer. Math. Soc. 145 (2017), 267-272 Request permission

Abstract:

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

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