1Dipartimento di Matematica Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino, Italy 2Dipartimento 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
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 $h^n$.
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
Affiliations des auteurs :
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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author = {Valentina Casarino and Paolo Ciatti},
title = {Transferring $L^p$ eigenfunction bounds
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journal = {Studia Mathematica},
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AU - Paolo Ciatti
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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
