The Hausdorff-Young inequality on Lie groups

TL;DR

This paper investigates the Hausdorff-Young inequality on Lie groups, establishing sharp constants for compact groups, extending results for the Heisenberg group, and providing universal bounds for all Lie groups.

Contribution

It introduces new sharp constants for compact Lie groups, extends known results to the Heisenberg group, and offers a universal lower bound for all Lie groups.

Findings

Sharp local central Hausdorff-Young constants for compact Lie groups

Extension of results to the Heisenberg group

Universal lower bound for the inequality constants in Lie groups

Abstract

We prove several results about the best constants in the Hausdorff-Young inequality for noncommutative groups. In particular, we establish a sharp local central version for compact Lie groups, and extend known results for the Heisenberg group. In addition, we prove a universal lower bound to the best constant for general Lie groups.