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Sobolev functions in the critical case are uniformly continuous in $ s$-Ahlfors regular metric spaces when $ s\le1$


Author: Xiaodan Zhou
Journal: Proc. Amer. Math. Soc. 145 (2017), 267-272
MSC (2010): Primary 46E35, 28A80
DOI: https://doi.org/10.1090/proc/13220
Published electronically: July 7, 2016
MathSciNet review: 3565378
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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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Additional Information

Xiaodan Zhou
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: xiz78@pitt.edu

DOI: https://doi.org/10.1090/proc/13220
Keywords: Sobolev functions, uniform continuity, fractals, Ahlfors regular
Received by editor(s): November 19, 2015
Received by editor(s) in revised form: March 8, 2016, and March 17, 2016
Published electronically: July 7, 2016
Additional Notes: The author was partially supported by NSF grant DMS-1500647 of Piotr Hajłasz.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2016 American Mathematical Society