What question did this study set out to answer?

The aim is to provide a simpler proof for the main theorem regarding completely bounded multipliers of the Fourier algebra linked to Lie groups of real rank one.

March 29, 2026Open Access

The Constants of Cowling and Haagerup

Key Points

The aim is to provide a simpler proof for the main theorem regarding completely bounded multipliers of the Fourier algebra linked to Lie groups of real rank one.
Presented a straightforward proof approach.
Focused on connected real Lie groups of real rank 1.
Analyzed specific cases of groups, including SO and exceptional group F4.
Confirmed the theorem's applicability to locally isomorphic groups such as SO.
Identified that for group F4(-20), the structure reduces to a specific case.
Enhanced understanding of the relationships between group properties and multipliers.

Abstract

In this article we give a simpler proof of the main theorem of M. Cowling and U. Haagerup, Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one, Invent.Math.96 (1989), 507-549, which reads as follows.Let G be a connected real Lie group of real rank 1 with finite centre.If G is locally isomorphic to SO 0while if G is the exceptional rank one group F 4(-20) , then G = 21 .

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