Oscillating multipliers on the Heisenberg group

E. K. Narayanan, and S. Thangavelu. "Oscillating multipliers on the Heisenberg group." Colloquium Mathematicae 90.1 (2001): 37-50. <http://eudml.org/doc/284281>.

@article{E2001,
abstract = {Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^\{-1/2\} sin√ℒ$ is bounded on $L^\{p\}(Hⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^\{p\}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.},
author = {E. K. Narayanan, S. Thangavelu},
journal = {Colloquium Mathematicae},
keywords = {subLaplacian; Bessel function; Cauchy problem; wave equation},
language = {eng},
number = {1},
pages = {37-50},
title = {Oscillating multipliers on the Heisenberg group},
url = {http://eudml.org/doc/284281},
volume = {90},
year = {2001},
}

TY - JOUR
AU - E. K. Narayanan
AU - S. Thangavelu
TI - Oscillating multipliers on the Heisenberg group
JO - Colloquium Mathematicae
PY - 2001
VL - 90
IS - 1
SP - 37
EP - 50
AB - Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{-1/2} sin√ℒ$ is bounded on $L^{p}(Hⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
LA - eng
KW - subLaplacian; Bessel function; Cauchy problem; wave equation
UR - http://eudml.org/doc/284281
ER -