By using the notion of contraction of Lie groups, we transfer estimates for joint spectral projectors from the unit complex sphere in 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-2,
author = {Valentina Casarino and Paolo Ciatti},
title = {Transferring $L^{p}$ eigenfunction bounds from $S^{2n+1}$ to hn},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {23-42},
zbl = {1178.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-2}
}
Valentina Casarino; Paolo Ciatti. Transferring $L^{p}$ eigenfunction bounds from $S^{2n+1}$ to hⁿ. Studia Mathematica, Tome 192 (2009) pp. 23-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm194-1-2/