The \(L^p\)-continuity of imaginary powers of the Dunkl harmonic oscillator

DOI10.1007/S13226-015-0128-5zbMath1364.42019OpenAlexW1240522664MaRDI QIDQ2628110

Hassen Tayari, Bechir Amri

Publication date: 12 June 2017

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13226-015-0128-5

zbMATH Keywords

singular integralsHermite polynomialsDunkl operators

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (3)

On harmonic analysis operators in Laguerre-Dunkl and Laguerre-symmetrized settings ⋮ Semigroup and Riesz transform for the Dunkl-Schrödinger operators ⋮ Dunkl-Schrödinger operators

Cites Work

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• Riesz transforms for Dunkl transform
• BMO results for operators associated to Hermite expansions
• A transference theorem for the Dunkl transform and its applications
• Imaginary powers of the Dunkl harmonic oscillator
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• Positivity of Dunkl's intertwining operator
• Convolution operator and maximal function for the Dunkl transform
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• On conjugate Poisson integrals and Riesz transforms for the Hermite expansions
• A positive radial product formula for the Dunkl kernel

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