Revista Matemática Iberoamericana

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Volume 34, Issue 3, 2018, pp. 1021–1054
DOI: 10.4171/RMI/1014

Published online: 2018-08-27

Intertwinings and generalized Brascamp–Lieb inequalities

Marc Arnaudon[1], Michel Bonnefont[2] and Aldéric Joulin[3]

(1) Université de Bordeaux I, Talence, France
(2) Université de Bordeaux I, Talence, France
(3) Université de Toulouse, France

We continue our investigation of the intertwining relations for Markov semigroups and extend our previous results to multi-dimensional diffusions. In particular these formulae entail new functional inequalities of Brascamp–Lieb type for log-concave distributions and beyond. Our results are illustrated by some classical and less classical examples.

Keywords: Intertwining, diffusion operator on vector fields, spectral gap, Brascamp–Lieb type inequalities, log-concave probability measure

Arnaudon Marc, Bonnefont Michel, Joulin Aldéric: Intertwinings and generalized Brascamp–Lieb inequalities. Rev. Mat. Iberoamericana 34 (2018), 1021-1054. doi: 10.4171/RMI/1014