Geodesic
Oscillating multipliers on the Heisenberg group
E. K. Narayanan 1   ; S. Thangavelu 1
1 Statistics and Mathematics Division Indian Statistical Institute 8th mile Mysore Road Bangalore 560 059, India
Colloquium Mathematicum, Tome 90 (2001) no. 1, pp. 37-50 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm90-1-3
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

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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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

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