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From Sobolev inequality to doubling


Authors: Lyudmila Korobenko, Diego Maldonado and Cristian Rios
Journal: Proc. Amer. Math. Soc. 143 (2015), 4017-4028
MSC (2010): Primary 35J70, 35J60, 35B65, 46E35, 31E05, 30L99
DOI: https://doi.org/10.1090/S0002-9939-2015-12556-7
Published electronically: March 18, 2015
MathSciNet review: 3359590
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Abstract: In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.


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Additional Information

Lyudmila Korobenko
Affiliation: Department of Mathematics, University of Calgary, Calgary, Alberta, Canada AB T2N 1N4
Email: lkoroben@ucalgary.ca

Diego Maldonado
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: dmaldona@math.ksu.edu

Cristian Rios
Affiliation: Department of Mathematics, University of Calgary, Calgary, Alberta, Canada AB T2N 1N4
Email: crios@ucalgary.ca

DOI: https://doi.org/10.1090/S0002-9939-2015-12556-7
Keywords: Sobolev inequality, Moser iteration, subunit metric spaces, doubling condition
Received by editor(s): December 1, 2013
Received by editor(s) in revised form: March 4, 2014, and June 4, 2014
Published electronically: March 18, 2015
Additional Notes: The second author was supported by the US National Science Foundation under grant DMS 1361754
The third author was supported by the Natural Sciences and Engineering Research Council of Canada
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2015 American Mathematical Society

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