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Transferring L p eigenfunction bounds from S 2 n + 1 to hⁿ

Valentina Casarino, Paolo Ciatti (2009)

Studia Mathematica

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 2 n + 1 in 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.

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