A sharp inequality and its applications

TL;DR

This paper proves a new sharp inequality involving exponential weights, which simplifies the proof of the Onofri inequality on the 2-sphere and has broader mathematical applications.

Contribution

It introduces a novel sharp inequality with exponential weights and demonstrates its application to proving the Onofri inequality on S^2.

Findings

Established a sharp analog Hardy inequality with exponential weights.

Provided a direct proof of the Onofri inequality on S^2.

Showcased applications of the new inequality in geometric analysis.

Abstract

We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n=2) leads to a direct proof of Onofri inequality on S^2.