Extremizability of Fourier restriction to the paraboloid

Abstract

In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in ${\mathbb{R}}^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result had previously been established for the case $q=2$. In the range where the boundedness of the restriction operator is still an open question, our result is conditional on improvements toward the restriction conjecture.

arXiv commentSome typos were corrected and arguments expanded in several places

References in corpus (4)

• A sharp bilinear restriction estimate for paraboloids
• A restriction estimate in ${\mathbb{R}}^3$ using brooms
• Weighted restriction estimates using polynomial partitioning
• Some recent progress on sharp Fourier restriction theory

Cited by in corpus (4)

• Extremizers for Adjoint Restriction to Pairs of Translated Paraboloids
• Extremals for $\alpha$-Strichartz inequalities
• Sharp Fourier extension on fractional surfaces
• On profile decomposition for Airy type equation