Abstract
We prove a nonlinear variant of the general Brascamp–Lieb inequality. Our proof consists of running an efficient, or “tight,” induction-on-scales argument, which uses the existence of Gaussian near-extremizers to the underlying linear Brascamp–Lieb inequality (Lieb’s theorem) in a fundamental way. A key ingredient is an effective version of Lieb’s theorem, which we establish via a careful analysis of near-minimizers of weighted sums of exponential functions. Instances of this inequality are quite prevalent in mathematics, and we illustrate this with some applications in harmonic analysis.
Original language | English |
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Pages (from-to) | 3291-3338 |
Number of pages | 48 |
Journal | Duke Mathematical Journal |
Volume | 169 |
Issue number | 17 |
Early online date | 16 Oct 2020 |
DOIs | |
Publication status | Published - 15 Nov 2020 |
Bibliographical note
39 pages. This article subsumes the results of arXiv:1801.05214 (https://arxiv.org/abs/1801.05214). Not yet published as of 02/11/2020.Keywords
- math.CA
- 42B37, 44A12, 52A40