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Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
-
Ali Baklouti
and
Junko Inoue
Published/Copyright:
November 18, 2010
Abstract
Let G be a connected and simply connected nilpotent Lie group, and m the dimension of the generic coadjoint orbits of G. Then it is proved in [Baklouti, Smaoui, Ludwig, J. Funct. Anal. 199: 508–520, 2003] that the operator value Fourier transform norm satisfies 
, where 
and q being the conjugate of p. When the assumption on G to be simply connected is removed, we prove an analogue estimate of type 
, where H designates the maximal compact central subgroup of G and m the dimension of generic coadjoint orbits of the universal covering of G. The case of non-simply connected Heisenberg groups is treated as an example.
Received: 2010-04-28
Revised: 2010-10-20
Published Online: 2010-11-18
Published in Print: 2011-September
© de Gruyter 2011
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- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
Keywords for this article
Nilpotent Lie group;
irreducible representation;
Fourier transform norm;
coadjoint orbit
Articles in the same Issue
- Geometric and harmonic analysis on homogeneous spaces
- On the multiplicity formula of compact nilmanifolds with flat orbits
- Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
- Atomic decomposition of a real Hardy space for Jacobi analysis
- Unitary holomorphic multiplier representations over a homogeneous bounded domain
- A deformation approach of the Kirillov map for exponential groups
- Visible actions on the non-symmetric homogeneous space SO(8, ℂ)/G2(ℂ)
- A Paley–Wiener theorem for some eigenfunction expansions
- Estimate of the Lp-Fourier transform norm for connected nilpotent Lie groups
