A Sharp analog of Young's Inequality on $S^N$ and Related Entropy Inequalities
Functional Analysis
2007-05-23 v1 Probability
Abstract
We prove a sharp analog of Young's inequality on , 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 to more than three functions, and leads to significant new information about the optimizers and the constants.
Keywords
Cite
@article{arxiv.math/0408030,
title = {A Sharp analog of Young's Inequality on $S^N$ and Related Entropy Inequalities},
author = {Eric Carlen and Elliott Lieb and Michael Loss},
journal= {arXiv preprint arXiv:math/0408030},
year = {2007}
}