Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates

DOI10.1080/10652469.2021.1913414zbMath1490.33003OpenAlexW3154135929MaRDI QIDQ5029046

Radouan Daher, Othman Tyr

Publication date: 11 February 2022

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2021.1913414

zbMATH Keywords

generalized translation operatorTitchmarsh's theoremLipschitz classDini-Lipschitz classFourier-Jacobi transformFourier-Jacobi operator

Mathematics Subject Classification ID

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) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (5)

Weighted integrability of Fourier-Dunkl transforms and generalized Lipschitz classes ⋮ Mellin integral transforms and generalized Lipschitz and Zygmund spaces ⋮ Weighted integrability results for first Hankel-Clifford transform ⋮ Weighted integrability of Fourier–Jacobi transforms ⋮ Dual Boas-type theorems and weighted integrability results for second Hankel-Clifford transform

Cites Work

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• Equivalence of \(K\)-functionals and modulus of smoothness generated by a generalized Jacobi-Dunkl transform on the real line
• Weighted approximation for the generalized discrete Fourier-Jacobi transform on space \(L_p(\mathbb{T})\)
• The convolution structure for Jacobi function expansions
• Index hypergeometric transform and imitation of analysis of Berezin kernels on hyperbolic spaces
• Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Jackson's type direct theorems

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