A general FB semigroup theorem produces multi-function sharp versions of hypercontractivity, Hausdorff-Young, log-Sobolev, and noisy Borell inequalities with necessary and sufficient Gaussian covariance conditions.
Adjoint Brascamp-Lieb inequalities
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abstract
The Brascamp-Lieb inequalities are a generalization of the H\"older, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of these inequalities, which can be viewed as an $L^p$ version of the entropy Brascamp-Lieb inequalities of Carlen and Cordero-Erausquin. As applications, we reprove a log-convexity property of the Gowers uniformity norms, and establish some reverse $L^p$ inequalities for various tomographic transforms. We conclude with some open questions.
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Multiversion of the Hausdorff--Young inequality
A general FB semigroup theorem produces multi-function sharp versions of hypercontractivity, Hausdorff-Young, log-Sobolev, and noisy Borell inequalities with necessary and sufficient Gaussian covariance conditions.