Transferring $L^p$ eigenfunction bounds from $S^{2n+1}$ to $h^n$

Volume 194 / 2009

Valentina Casarino, Paolo Ciatti Studia Mathematica 194 (2009), 23-42 MSC: 43A80, 43A85, 42B10. DOI: 10.4064/sm194-1-2


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 $h^n$.


  • Valentina CasarinoDipartimento di Matematica
    Politecnico di Torino
    Corso Duca degli Abruzzi 24
    10129 Torino, Italy
  • Paolo CiattiDipartimento di Metodi e Modelli Matematici
    per le Scienze Applicate
    Via Trieste 63
    35121 Padova, Italy

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