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A sharp analog of Young’s inequality on SN and related entropy inequalities
Journal article   Peer reviewed

A sharp analog of Young’s inequality on SN and related entropy inequalities

E Carlen, E Lieb and M Loss
The Journal of geometric analysis, Vol.14(3), pp.487-520
09/2004
DOI: https://doi.org/10.1007/BF02922101

Abstract

43A15 52A40 82C40 Abstract Harmonic Analysis best constants Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory entropy Fourier Analysis Global Analysis and Analysis on Manifolds Inequalities Mathematics optimizers
We prove a sharp analog of Young’s inequality on SN, 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 RN to more than three functions, and leads to significant new information about the optimizers and the constants.

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