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Positive Gaussian Kernels also Have Gaussian Minimizers
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eBook
Positive Gaussian Kernels also Have Gaussian Minimizers
2022
Overview
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.
Publisher
American Mathematical Society
Subject
ISBN
9781470451431, 1470451433
