An LP version of Hardy's theorem for the Dunkl transform

DOI10.1017/S1446788700014518zbMath1084.44001OpenAlexW2121494985MaRDI QIDQ4658696

Khalifa Trimèche, Léonard Gallardo

Publication date: 18 March 2005

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

Full work available at URL: https://doi.org/10.1017/s1446788700014518

zbMATH Keywords

Dunkl transformdifferential-difference operatorsreflections groupsspecial Lebesgue spaces

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral transforms of special functions (44A20) Other transforms and operators of Fourier type (43A32) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Reflection groups, reflection geometries (51F15)

Related Items (21)

Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line ⋮ Cowling-Price type theorem related to Bessel-Struve transform ⋮ The Beurling theorem in space-time algebras ⋮ Beurling's theorem in the Clifford algebras ⋮ Qualitative uncertainty principles for the windowed Opdam–Cherednik transform on weighted modulation spaces ⋮ Restriction theorem for the Fourier-Dunkl transform and its applications to Strichartz inequalities ⋮ The two-sided quaternionic Dunkl transform and Hardy's theorem ⋮ A variant of Cowling-Price's theorem for the Dunkl transform on \(\mathbb R\) ⋮ Qualitative uncertainty principles for the Opdam–Cherednik transform ⋮ Pitt's inequalities for the Dunkl transform on ℝ^d ⋮ Uncertainty principles for the Opdam–Cherednik transform on modulation spaces ⋮ Miyachi's theorem for the Dunkl transform ⋮ QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM ⋮ Uncertainty principles for the generalized Fourier transform associated to a Dunkl-type operator ⋮ Uncertainty principles involvingL¹-norms for the Dunkl transform ⋮ Dunkl-Schrödinger semigroups and applications ⋮ Dunkl heat semigroup and applications ⋮ Cowling-Price's and Hardy's uncertainty principles for the generalized Fourier transform associated to a Cherednik type operator on the real line ⋮ Qualitative uncertainty principles for the hypergeometric Fourier transform ⋮ Revisiting Beurling's theorem for Fourier–Dunkl transform ⋮ A variant of Hardy's and Miyachi's theorems for the Bessel–Struve transform

Cites Work

• Generalized Hermite polynomials and the heat equation for Dunkl operators
• The Dunkl transform
• An analogue of Hardy's theorem for the Dunkl transform
• Uncertainty principles on certain Lie groups
• Exact operator solution of the Calogero-Sutherland model
• Positivity of Dunkl's intertwining operator
• An elementary approach to the hypergeometric shift operators of Opdam
• Integral Kernels with Reflection Group Invariance
• The dunkel intertwining operator on spaces of functions and distributions and integral representation of its dual
• Dunkl Operator Formalism for Quantum Many-Body Problems Associated with Classical Root Systems
• A Theorem Concerning Fourier Transforms

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