Harmonic analysis associated with the one-dimensional Dunkl transform

DOI10.1007/s00365-013-9179-1zbMath1269.42018OpenAlexW2043078875MaRDI QIDQ1943996

Zhongkai Li, Jianquan Liao

Publication date: 3 April 2013

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-013-9179-1

zbMATH Keywords

Hardy spaceDunkl transform\(\lambda\)-Hilbert transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Conjugate functions, conjugate series, singular integrals (42A50) Generalizations of Bers and Vekua type (pseudoanalytic, (p)-analytic, etc.) (30G20) Hardy spaces (30H10)

Related Items (12)

A multiplier theorem for the Hankel transform on the associated Hardy space ⋮ Generalized Dunkl-Lipschitz spaces ⋮ Weyl transforms associated with Dunkl wavelet transform ⋮ Lipschitz and Triebel-Lizorkin spaces, commutators in Dunkl setting ⋮ Equivalence of \(K\)-functionals and modulus of smoothness generated by a Dunkl type operator on the interval \((-1, 1)\) ⋮ On Schrödinger oscillatory integrals associated with the Dunkl transform ⋮ On fundamental harmonic analysis operators in certain Dunkl and Bessel settings ⋮ A characterization of the Hardy space associated with the Dunkl transform ⋮ ON LITTLEWOOD–PALEY FUNCTIONS ASSOCIATED WITH THE DUNKL OPERATOR ⋮ Hörmander's multiplier theorem for the Dunkl transform ⋮ Appell-Dunkl sequences and Hurwitz-Dunkl zeta functions ⋮ The dual of the Hardy space associated with the Dunkl operators

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