Hilbert transform and related topics associated with Jacobi–Dunkl operators of compact and noncompact types

DOI10.1515/APAM.2010.035zbMath1228.44005MaRDI QIDQ3093135

Taha Samaali, Néjib Ben Salem

Publication date: 12 October 2011

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hilbert transformPoisson integralweighted Lebesgue spacesJacobi polynomialJacobi functionsconjugate Poisson integralconjugate function operatorheat integralJacobi-Dunkl LaplacianJacobi-Dunkl polynomial

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items (3)

A new aspect of generalized integral operator and an estimation in a generalized function theory ⋮ Spectral properties of differential-difference symmetrized operators ⋮ Harmonic analysis associated with the Jacobi-Dunkl operator on \((-\pi, \pi)\): exotic cases

Cites Work

• Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\)
• Riesz transform and \(g\)-function associated with Bessel operators and their appropriate Banach spaces
• Riesz transforms for Jacobi expansions
• Asymptotics of polynomials orthogonal with respect to a discrete-complex Sobolev inner product
• The heat semigroup for the Jacobi-Dunkl operator and the related Markov processes
• POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$
• AnL^pversion of Hardy's theorem for the Jacobi–Dunkl transform
• ON LITTLEWOOD-PALEY FUNCTIONS ASSOCIATED WITH BESSEL OPERATORS

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