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 condition, either with and , or with and . As such, results are valid in the case of a Riemannian manifold, which constitutes a generalization of what was previously proved.
Citation
Ivan Gentil. Simon Zugmeyer. "A family of Beckner inequalities under various curvature-dimension conditions." Bernoulli 27 (2) 751 - 771, May 2021. https://doi.org/10.3150/20-BEJ1228
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