Lieb-Thirring inequalities and other functional inequalities for orthonormal systems

TL;DR

This paper reviews recent advances in functional inequalities for orthonormal systems, highlighting how orthonormality yields improvements over classical inequalities for operators related to Sobolev and Fourier restriction inequalities.

Contribution

It presents new insights into how orthonormality enhances functional inequalities for specific operators, expanding understanding in this area.

Findings

Orthonormality leads to gains over triangle inequality applications.

Results apply to operators related to Sobolev inequalities.

Results also extend to Fourier restriction inequalities.

Abstract

We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators under consideration are either related to Sobolev type inequalities or to Fourier restriction type inequalities.