Positive Gaussian Kernels Also Have Gaussian Minimizers (Memoirs of the American Mathematical Society)

Barthe, Franck/ Wolff, Pawel

American Mathematical Society（2022/06発売）

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製本 Paperback:紙装版/ペーパーバック版／ページ数 90 p.
言語 ENG
商品コード 9781470451431
DDC分類 519.2

Full Description

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 wegive 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 severalinverse inequalities.