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

• Autorzy: Valentina Casarino , Paolo Ciatti
• Języki publikacji: EN

Abstrakty

EN

By using the notion of contraction of Lie groups, we transfer $L^{p} - L²$ estimates for joint spectral projectors from the unit complex sphere $S^{2n+1}$ in $ℂ^{n+1}$ 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.

Kategorie tematyczne

• 43A80: Analysis on other specific Lie groups
• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 43A85: Analysis on homogeneous spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 194
• Numer: 1
• Strony: 23-42

Daty

wydano

2009

Twórcy

autor

Valentina Casarino

• Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

autor

Paolo Ciatti

• Dipartimento di Metodi e Modelli Matematici, per le Scienze Applicate, Via Trieste 63, 35121 Padova, Italy

Identyfikatory

DOI

10.4064/sm194-1-2