A Sharp analog of Young's Inequality on S^N and Related Entropy Inequalities

2004/08/02 by Eric Carlen, Elliott Lieb, Michael Loss · 4 citations
Mathematics · #math.FA #math.PR #msc:43A15 #msc:52A40 #msc:82C40

paper · pdf

published as Jour. Geometry and Analysis vol 14, no. 3, 487-520 (2004).

arxiv created 2004/08/02 · arxiv updated 2009/12/01

Abstract

We prove a sharp analog of Young's inequality on S^N, and deduce from it certain sharp entropy inequalities. The proof turns on constructing a nonlinear heat flow that drives trial functions to optimizers in a monotonic manner. This strategy also works for the generalization of Young's inequality on R^N to more than three functions, and leads to significant new information about the optimizers and the constants.

Cited by

• Operator capacity, the Brascamp--Lieb inequality and geometric programming
• Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
• Multiversion of the Hausdorff--Young inequality
• A parabolic PDE-based approach to Borell–Brascamp–Lieb inequality

Related

• Heat equation and the sharp Young's inequality
• Heat equation and convolution inequalities
• Yet Another Proof of the Entropy Power Inequality
• Entropy flows and functional inequalities in convex sets
• Near-extremizers of Young's Inequality for R^d