On the existence of maximizers for a family of Restriction Theorems

TL;DR

This paper investigates the existence of maximizers for a broad class of restriction operators, establishing their existence away from the end-point and providing counterexamples at the end-point.

Contribution

It proves the existence of maximizers for a general family of restriction operators up to the end-point and offers counterexamples at the end-point.

Findings

Maximizers exist for the restriction operators away from the end-point.

Counterexamples show non-existence at the end-point.

Provides a comprehensive understanding of the behavior of restriction operators.

Abstract

We prove the existence of maximizers for a general family of restrictions operators, up to the end-point. We also provide some counterxamples in the end-point case.