A family of Beckner inequalities under various curvature-dimension conditions
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].
Origin : Files produced by the author(s)
Loading...