Nonexistence of extremals for the adjoint restriction inequality on the hyperboloid

Abstract

We study the problem of existence of extremizers for the $L^2$ to $L^p$ adjoint Fourier restriction inequalities on the hyperboloid in dimensions 3 and 4, in which cases $p$ is an even integer. We will use the method developed by Foschi to show that extremizers do not exist.

32 pages. Correction for Theorem 1.2 and Proposition 7.5 and addition of Remark 1.3

References in corpus (4)

• A sharp inequality for the Strichartz norm
• On extremizing sequences for the adjoint restriction inequality on the cone
• On the existence of maximizers for a family of Restriction Theorems
• Existence of Extremals for a Fourier Restriction Inequality

Cited by in corpus (11)

• Extremizers for Fourier restriction on hyperboloids
• Sharp mixed norm spherical restriction
• Some sharp bilinear space-time estimates for the wave equation
• Nonexistence of extremizers for certain convex curves
• On extremizers for Strichartz estimates for higher order Schrödinger equations
• A comparison principle for convolution measures with applications
• Bilinear identities involving the $k$-plane transform and Fourier extension operators
• Some recent progress on sharp Fourier restriction theory
• Extremizers for Fourier restriction inequalities: convex arcs
• On profile decomposition for Airy type equation
• A Sharp Sobolev--Strichartz estimate for the wave equation