Random-Weighted Sobolev Inequalities on $${\mathbb{R}^d }$$ R d and Application to Hermite Functions

2014 ◽  
Vol 16 (2) ◽  
pp. 651-689 ◽  
Author(s):  
Aurélien Poiret ◽  
Didier Robert ◽  
Laurent Thomann
Keyword(s):  
Hermite Functions ◽  
Sobolev Inequalities ◽  
Weighted Sobolev Inequalities

Uniform L 2 -Weighted Sobolev Inequalities

1991 ◽  
Vol 112 (1) ◽  
pp. 53 ◽  
Author(s):  
Filippo Chiarenza ◽  
Alberto Ruiz
Keyword(s):  
Sobolev Inequalities ◽  
Weighted Sobolev Inequalities

scholarly journals Weighted Sobolev Inequalities in CD(0,N) spaces

2020 ◽  
Author(s):  
David Tewodrose
Keyword(s):  
Heat Kernel ◽  
Growth Condition ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Sobolev Inequalities ◽  
Uniform Bound ◽  
Nash Inequality ◽  
Weighted Sobolev Inequalities

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 Minerbe 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.

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