Stability of the Brascamp-Lieb constant and applications
Jonathan Bennett, Neal Bez, Taryn C. Flock, Sanghyuk Lee
TL;DR
This paper proves the local boundedness of the optimal constant in the Brascamp-Lieb inequality and applies this to derive new Fourier restriction, Kakeya-type, and nonlinear inequalities in harmonic analysis.
Contribution
It establishes the local boundedness of the Brascamp-Lieb constant and introduces generalized inequalities with broad applications in harmonic analysis.
Findings
The Brascamp-Lieb constant is locally bounded as a function of the linear transformations.
Derived new Fourier restriction inequalities.
Established nonlinear variants of the Brascamp-Lieb inequality.
Abstract
We prove that the best constant in the general Brascamp-Lieb inequality is a locally bounded function of the underlying linear transformations. As applications we deduce certain very general Fourier restriction, Kakeya-type, and nonlinear variants of the Brascamp-Lieb inequality which have arisen recently in harmonic analysis.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.