We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb's results on maximizers of multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends several inverse inequalities.

About the Author
Franck Barthe, Universite de Toulouse, France.

Pawel Wolff, Universite de Toulouse, France.


Book Information
ISBN 9781470451431
Author Franck Barthe
Format Paperback
Page Count 90
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 194g