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Comptes Rendus. Mathématique
Harmonic analysis
Lipschitz Conditions in Damek–Ricci Spaces
Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 675-685.

In this paper we extend classical Titchmarsh theorems on the Fourier–Helgason transform of Lipschitz functions to the setting of L p -space on Damek–Ricci spaces. As consequences, quantitative Riemann–Lebesgue estimates are obtained and an integrability result for the Fourier–Helgason transform is developed extending ideas used by Titchmarsh in the one dimensional setting.

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DOI: https://doi.org/10.5802/crmath.211
Classification: 43A30,  42B10
Salah El Ouadih 1; Radouan Daher 2

1. Laboratory MC, Polydisciplinary Faculty of Safi, Cadi Ayyad University, Marrakech, Morocco
2. Laboratory TAGMD, Faculty of Sciences Aïn Chock, Hassan II University, Casablanca, Morocco
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     journal = {Comptes Rendus. Math\'ematique},
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Salah El Ouadih; Radouan Daher. Lipschitz Conditions in Damek–Ricci Spaces. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 675-685. doi : 10.5802/crmath.211. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.211/

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