A family of Beckner inequalities under various curvature-dimension conditions
Résumé
In this paper, we offer a proof for a family of functional inequalities interpolating between the Poincaré and the logarithmic Sobolev (standard and weighted) inequalities. The proofs rely both on entropy flows and on a CD(ρ,n) condition, either with ρ=0 and n>0, or with ρ>0 and n∈R. As such, results are valid in the case of a Riemannian manifold, which constitutes a generalization of what was previously proved.
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| Commentaire | Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing) |
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