Fourier duality in the Brascamp-Lieb inequality

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  • Korea Institute for Advanced Study


It was observed recently in work of Bez, Buschenhenke, Cowling, Flock and the first author, that the euclidean Brascamp-Lieb inequality satisfies a natural and useful Fourier duality property. The purpose of this paper is to establish an appropriate discrete analogue of this. Our main result identifies the Brascamp-Lieb constants on (finitely-generated) discrete abelian groups with Brascamp-Lieb constants on their (Pontryagin) duals. As will become apparent, the natural setting for this duality principle is that of locally compact abelian groups, and this raises basic questions about Brascamp-Lieb constants formulated in this generality.


Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusPublished - 27 Sep 2021