Dimensional variance inequalities of Brascamp-Lieb type and a local approach to dimensional Prékopa's theorem

2013/02/19 by Van Hoang Nguyen, Nguyen, Van Hoang · 1 citation
Mathematics · #26A51 #52A40 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26A51 #msc:52A40

paper · pdf · doi:10.48550/arxiv.1302.4589

24 pages, some minor corrections. To appear in Journal of Functional Analysis

arxiv created 2013/11/05 · arxiv updated 2013/11/06

Abstract

We give a new approach, inspired by Hörmander's L²-method, to weighted variance inequalities which extend results obtained by Bobkov and Ledoux. It provides in particular a local proof of the dimensional functional forms of the Brunn-Minkowski inequalities. We also present several applications of these variance inequalities, including reverse Hölder inequalities for convex functions, weighted Brascamp-Lieb inequalities and sharp weighted Poincaré inequalities for generalized Cauchy measures.

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