The optimal constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group

TL;DR

This paper finds the best constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group and characterizes the functions where equality is achieved.

Contribution

It determines the optimal constant and identifies extremal functions for the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group.

Findings

Established the sharp constant in the inequality

Characterized functions attaining equality

Contributed to understanding geometric inequalities on quaternionic groups

Abstract

We determine the best (optimal) constant in the $L^2$ Folland-Stein inequality on the quaternionic Heisenberg group and the non-negative functions for which equality holds.