Open AccessPositive Gaussian Kernels also Have Gaussian Minimizers
Author(s) -
Franck Barthe,
Paweł Wolff
Publication year - 2022
Publication title -
memoirs of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.034
H-Index - 70
eISSN - 1947-6221
pISSN - 0065-9266
DOI - 10.1090/memo/1359
Subject(s) - multilinear map , mathematics , gaussian , constant (computer programming) , lp space , pure mathematics , inverse , mathematical analysis , computer science , banach space , geometry , physics , quantum mechanics , programming language
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.