| Issue |
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|---|---|---|
| Article Number | S22 | |
| Number of page(s) | 19 | |
| DOI | https://doi.org/10.1051/cocv/2020080 | |
| Published online | 01 March 2021 | |
Weighted Sobolev inequalities in CD(0, N) spaces
CY Cergy Paris University,
95000
Cergy, France.
* Corresponding author: david.tewodrose@cyu.fr
Received:
8
November
2019
Accepted:
18
November
2020
In this note, we prove global weighted Sobolev inequalities on non-compact CD(0, N) spaces satisfying a suitable growth condition, extending to possibly non-smooth and non-Riemannian structures a previous result from [V. Minerbe, G.A.F.A. 18 (2009) 1696–1749] stated for Riemannian manifolds with non-negative Ricci curvature. We use this result in the context of RCD(0, N) spaces to get a uniform bound of the corresponding weighted heat kernel via a weighted Nash inequality.
Mathematics Subject Classification: 46E36 / 53C23 / 35K08 / 51K10
Key words: Sobolev inequalities / metric measure spaces#curvature-dimension conditions / heat kernel
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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