Existence of maximizers for Sobolev-Strichartz inequalities

TL;DR

This paper proves the existence of maximizers for Sobolev-Strichartz inequalities across various propagators, including wave, Dirac, and hyperbolic Schrödinger flows, advancing understanding in harmonic analysis.

Contribution

It establishes the existence of maximizers for a broad class of Sobolev-Strichartz estimates, covering multiple important propagators.

Findings

Maximizers exist for Sobolev-Strichartz inequalities.

Results apply to wave, Dirac, and hyperbolic Schrödinger flows.

Advances the theoretical understanding of dispersive PDEs.

Abstract

We prove the existence of maximizers of Sobolev-Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrodinger flows.