Sharp Hardy-Littlewood-Sobolev Inequalities on Octonionic Heisenberg Group

TL;DR

This paper establishes sharp Hardy-Littlewood-Sobolev inequalities on the octonionic Heisenberg group, extending previous work on groups of Heisenberg type and building on foundational results by Frank and Lieb.

Contribution

It introduces the first sharp Hardy-Littlewood-Sobolev inequalities specifically for the octonionic Heisenberg group, expanding the scope of known inequalities to new algebraic structures.

Findings

Derived sharp inequalities for the octonionic Heisenberg group

Extended previous results from groups of Heisenberg type

Built upon foundational work by Frank and Lieb

Abstract

This paper is a second one following our work [CLZ13] in series, considering sharp Hardy- Littlewood-Sobolev inequalities on groups of Heisenberg type. The first important breakthrough was made by Frank and Lieb in [FL12]. In this paper, analogous results are obtained for octonionic Heisenberg group.