Weighted Sobolev inequalities in CD(0, N ) spaces

Weighted Sobolev inequalities in CD(0, N ) spaces

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 no...

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2021, Vol.27, p.S22
1. Verfasser: Tewodrose, David
Format: Artikel
Sprache:eng
Schlagworte:
Inequalities
Mathematics
Riemann manifold
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Zusammenfassung: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.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2020080