Abstract
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.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
Cited by
2 articles.
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1. Adimensional weighted Sobolev inequalities in PI spaces;Annales Fennici Mathematici;2022-01-28
2. Weighted Sobolev inequalities in CD(0, N) spaces;ESAIM: Control, Optimisation and Calculus of Variations;2021