Hardy-Type Inequalities for Fractional Powers of the Dunkl–Hermite Operator

DOI10.1017/S0013091517000311zbMath1435.26013arXiv1602.04997OpenAlexW2963771901MaRDI QIDQ5228162

Luz Roncal, Óscar Ciaurri, Sundaram Thangavelu

Publication date: 9 August 2019

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.04997

zbMATH Keywords

heat semigroupHardy inequalityDunkl harmonic oscillatorfractional order operatorLaguerre expansions

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Harmonic analysis and spherical functions (43A90) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (10)

Hardy's inequality for the fractional powers of a discrete Laplacian ⋮ Hardy inequalities for the fractional powers of the Grushin operator ⋮ The Hardy inequality and fractional Hardy inequality for the Dunkl Laplacian ⋮ Hardy's inequality for the fractional powers of the Grushin operator ⋮ An extension problem, trace Hardy and Hardy's inequalities for the Ornstein-Uhlenbeck operator ⋮ Sharp Hardy's inequality for orthogonal expansions in \(H^p\) spaces ⋮ A Hardy inequality for ultraspherical expansions with an application to the sphere ⋮ Unnamed Item ⋮ Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities ⋮ An Extension Problem and Hardy Type Inequalities for the Grushin Operator

Uses Software

• DLMF

Cites Work

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• Pitt's Inequality and the Uncertainty Principle
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Mixed norm estimates for the Cesàro means associated with Dunkl–Hermite expansions

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