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Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types
-
Néjib Ben Salem
and
Taha Samaali
Published/Copyright:
September 17, 2010
Abstract
We define conjugate function operators (called also “Hilbert transform”), Poisson and conjugate Poisson integrals associated with the Jacobi–Dunkl Laplacians on 
and on ℝ. We prove that these operators satisfy Lp-boundedness, 1 < p < +∞, in appropriate Lebesgue weighted spaces.
Keywords.: Jacobi–Dunkl Laplacian; Jacobi functions; Jacobi polynomial; Jacobi–Dunkl polynomial; heat integral; Poisson integral; conjugate function operator; conjugate Poisson integral
Received: 2010-04-25
Revised: 2010-10-28
Published Online: 2010-09-17
Published in Print: 2011-September
© de Gruyter 2011
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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
Keywords for this article
Jacobi–Dunkl Laplacian;
Jacobi functions;
Jacobi polynomial;
Jacobi–Dunkl polynomial;
heat integral;
Poisson integral;
conjugate function operator;
conjugate Poisson integral
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
