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.
ISBN: | 9781470451431 |
Publication date: | 30th June 2022 |
Author: | Franck Barthe, Pawel Wolff |
Publisher: | American Mathematical Society |
Format: | Paperback |
Pagination: | 90 pages |
Series: | Memoirs of the American Mathematical Society |
Genres: |
Probability and statistics |