Fourier duality in the Brascamp-Lieb inequality
Research output: Contribution to journal › Article › peer-review
Colleges, School and Institutes
- 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.
|Number of pages||23|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 27 Sep 2021|