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

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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Valentina Casarino, and Paolo Ciatti. "Transferring $L^{p}$ eigenfunction bounds from $S^{2n+1}$ to hⁿ." Studia Mathematica 194.1 (2009): 23-42. <http://eudml.org/doc/284497>.

@article{ValentinaCasarino2009,
abstract = {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.},
author = {Valentina Casarino, Paolo Ciatti},
journal = {Studia Mathematica},
keywords = {Lie groups contraction; complex spheres; reduced Heisenberg group; joint spectral projectors; discrete restriction theorem},
language = {eng},
number = {1},
pages = {23-42},
title = {Transferring $L^\{p\}$ eigenfunction bounds from $S^\{2n+1\}$ to hⁿ},
url = {http://eudml.org/doc/284497},
volume = {194},
year = {2009},
}

TY - JOUR
AU - Valentina Casarino
AU - Paolo Ciatti
TI - Transferring $L^{p}$ eigenfunction bounds from $S^{2n+1}$ to hⁿ
JO - Studia Mathematica
PY - 2009
VL - 194
IS - 1
SP - 23
EP - 42
AB - 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.
LA - eng
KW - Lie groups contraction; complex spheres; reduced Heisenberg group; joint spectral projectors; discrete restriction theorem
UR - http://eudml.org/doc/284497
ER -

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