Sharp Beckner-type inequalities for Cauchy and spherical distributions
Abstract
Using some harmonic extensions on the upper-half plane, and probabilistic representations, and curvature-dimension inequalities with some negative dimensions, we obtain some new opimal functional inequalities of the Beckner type for the Cauchy type distributions on the Euclidean space. These optimal inequalities appear to be equivalent to some non tight optimal Beckner inequalities on the sphere, and the family appear to be a new form of the Sobolev inequality.
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Comment : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing).
Comment : Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing).
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