Transferring $L^p$ eigenfunction bounds from $S^{2n+1}$ to $h^n$
Volume 194 / 2009
Studia Mathematica 194 (2009), 23-42
MSC: 43A80, 43A85, 42B10.
DOI: 10.4064/sm194-1-2
Abstract
By using the notion of contraction of Lie groups, we transfer $L^p$-$L^2$ estimates for joint spectral projectors from the unit complex sphere $S^{2n+1}$ in ${\mathbb C}^{n+1}$ to the reduced Heisenberg group $h^{n}$. In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on $h^n$. As a consequence, we prove, in the spirit of Sogge's work, a discrete restriction theorem for the sub-Laplacian $L$ on $h^n$.
