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Journal Articles Bernoulli Year : 2021

A family of Beckner inequalities under various curvature-dimension conditions

Ivan Gentil
Simon Zugmeyer
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Abstract

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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Dates and versions

hal-02052691 , version 1 (28-02-2019)

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Ivan Gentil, Simon Zugmeyer. A family of Beckner inequalities under various curvature-dimension conditions. Bernoulli, 2021, 27 (2), pp.751-771. ⟨10.3150/20-BEJ1228⟩. ⟨hal-02052691⟩
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