Geodesic
Transferring $L^p$ eigenfunction bounds from $S^{2n+1}$ to $h^n$
Valentina Casarino 1   ; Paolo Ciatti 2
1 Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy
2 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate Via Trieste 63 35121 Padova, Italy
Studia Mathematica, Tome 194 (2009) no. 1, pp. 23-42 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $h^n$.
DOI : 10.4064/sm194-1-2
Keywords: using notion contraction lie groups transfer p l estimates joint spectral projectors unit complex sphere mathbb reduced heisenberg group particular deduce estimates recently obtained koch ricci consequence prove spirit sogges work discrete restriction theorem sub laplacian

Valentina Casarino  1   ; Paolo Ciatti  2

1 Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy
2 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate Via Trieste 63 35121 Padova, Italy 
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Valentina Casarino; Paolo Ciatti. Transferring $L^p$ eigenfunction bounds
from $S^{2n+1}$ to $h^n$. Studia Mathematica, Tome 194 (2009) no. 1, pp. 23-42. doi: 10.4064/sm194-1-2

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