Let ${\cal L} $ be the sublaplacian on the Heisenberg group
$ H^n$. A recent result of Müller and Stein shows
that the operator $ {{\cal L}}^{-1/2} \mathop {\rm sin}\nolimits
\sqrt{{\cal L}} $ is bounded on $ L^p(H^n) $ 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.
Keywords:
cal sublaplacian heisenberg group recent result ller stein shows operator cal mathop sin nolimits sqrt cal bounded n satisfying p paper operator bounded bigger range p n consider only functions which band limited central variable
Affiliations des auteurs :
E. K. Narayanan
1
;
S. Thangavelu
1
1
Statistics and Mathematics Division Indian Statistical Institute 8th mile Mysore Road Bangalore 560 059, India
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author = {E. K. Narayanan and S. Thangavelu},
title = {Oscillating multipliers on {the
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journal = {Colloquium Mathematicum},
pages = {37--50},
year = {2001},
volume = {90},
number = {1},
doi = {10.4064/cm90-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm90-1-3/}
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AU - E. K. Narayanan
AU - S. Thangavelu
TI - Oscillating multipliers on the
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JO - Colloquium Mathematicum
PY - 2001
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%A S. Thangavelu
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Heisenberg group
%J Colloquium Mathematicum
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E. K. Narayanan; S. Thangavelu. Oscillating multipliers on the
Heisenberg group. Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 37-50. doi: 10.4064/cm90-1-3
