Extremisers for the trace theorem on the sphere

TL;DR

This paper characterizes all extremisers for the trace theorem on the sphere and provides sharp extension results for functions with specific Sobolev space regularity, advancing understanding of boundary behavior in harmonic analysis.

Contribution

It identifies all extremisers for the sphere trace theorem and establishes sharp extension results for Sobolev functions with angular regularity, a novel contribution in harmonic analysis.

Findings

Complete classification of extremisers for the trace theorem on the sphere.

Sharp extension inequalities for Sobolev functions with angular regularity.

Enhanced understanding of boundary behavior in harmonic analysis.

Abstract

We find all extremisers for the trace theorem on the sphere. We also provide a sharp extension for functions belonging to certain Sobolev spaces with angular regularity.