Théorème central limite sur les groupes nilpotents
By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in to the reduced Heisenberg group hⁿ. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on hⁿ. As a consequence, we prove, in the spirit of Sogge’s work, a discrete restriction theorem for the sub-Laplacian L on hⁿ.
It is shown that if G is a weakly amenable unimodular group then the Banach algebra , where is the Figà-Talamanca-Herz Banach algebra of G, is a dual Banach space with the Radon-Nikodym property if 1 ≤ r ≤ max(p,p’). This does not hold if p = 2 and r > 2.