Stability for Strichartz inequalities: Existence of minimizers

TL;DR

This paper investigates the stability of Strichartz inequalities related to Fourier restriction problems, demonstrating the existence of minimizers under certain conditions, especially for the paraboloid and two-dimensional sphere cases.

Contribution

It proves the existence of minimizers for the sharp constants in Strichartz inequalities, extending the understanding of stability and minimizer existence in Fourier restriction contexts.

Findings

Minimizers exist when sharp constants are below spectral-gap constants.

Existence of minimizers established for the two-dimensional sphere case.

Provides conditions under which stability inequalities admit minimizers.

Abstract

We study the quantitative stability associated with the adjoint Fourier restriction inequality, focusing on the paraboloid and two-dimensional sphere cases. We show that these Strichartz-stability inequalities admit minimizers attaining their sharp constants, provided that these sharp constants are strictly smaller than the corresponding spectral-gap constants. Furthermore, for the two-dimensional sphere case, we obtain the existence of minimizers.