Work

On the nonlinear Brascamp–Lieb inequality

Year: 2020

Type: article

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.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2020-0027

Authors: Jonathan Bennett, Neal Bez, Stefan Buschenhenke, Michael G. Cowling, Taryn C. Flock

Institutions: Saitama University, University of Birmingham, Christian-Albrechts-Universität zu Kiel, UNSW Sydney

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Australian Research Council, Japan Society for the Promotion of Science, FP7 Ideas: European Research Council