
Journal of Lie Theory 18 (2008), No. 3, 627644 Copyright Heldermann Verlag 2008 The Constants of Cowling and Haagerup Varadharajan Muruganandam Dept. of Mathematics, Pondicherry University, Pondicherry 605 014, India vmuruganandam@gmail.com [Abstractpdf] 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) 507549], 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$_0(1,n)$ or SU$(1,n)$, then $\Lambda_G = 1$. If $G$ is locally isomorphic to Sp$(1,n)$, then $\Lambda_G = 2n1$, while if $G$ is the exceptional rank one group $F_{4(20)}$, then $\Lambda_G = 21$. Keywords: Fourier algebra, weak amenability, Gelfand pair, hypergroup. MSC: 43A30, 22D25, 43A62, 43A90, 43A22 [ Fulltextpdf (242 KB)] for subscribers only. 