Sharp quantitative integral inequalities for general conformally invariant extensions

TL;DR

This paper establishes sharp integral inequalities for conformally invariant extension operators by refining hypergeometric function analysis, extending prior results to a broader parameter range.

Contribution

It introduces a refined hypergeometric analysis to derive sharp inequalities for a general class of conformally invariant operators, broadening the applicable parameter range.

Findings

Derived sharp integral inequalities for conformally invariant extensions.

Extended previous results to full admissible parameter ranges.

Provided a new analytical framework using hypergeometric functions.

Abstract

In this paper, we develop a refined analysis of hypergeometric functions to establish sharp quantitative integral inequalities for a general family of conformally invariant extension operators and their adjoints. Our results extend the recent work of Frank, Peteranderl, and Read \cite{Frank&Peteranderl&Read} to the full admissible parameter range under the natural index constraints.