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Positive Gaussian Kernels Also Have Gaussian Minimizers

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Positive Gaussian Kernels Also Have Gaussian Minimizers Synopsis

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 This Edition

ISBN: 9781470451431
Publication date:
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