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A family of Beckner inequalities under various curvature-dimension conditions

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Ivan Gentil
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  • PersonId : 828908
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 to what was proved in [BGS18, Ngu18].
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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. 2019. ⟨hal-02052691⟩
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