Lipschitz Conditions in Damek–Ricci Spaces

Salah El Ouadih; Radouan Daher

doi:10.5802/crmath.211

Analyse harmonique

Lipschitz Conditions in Damek–Ricci Spaces

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

Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 675-685.

Résumé

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.

Reçu le : 2021-01-19
Révisé le : 2021-04-07
Accepté le : 2021-04-07
Publié le : 2021-08-25

DOI : 10.5802/crmath.211

Classification : 43A30, 42B10

Affiliations des auteurs :

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

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Salah El Ouadih and Radouan Daher},
     title = {Lipschitz {Conditions} in {Damek{\textendash}Ricci} {Spaces}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {675--685},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {6},
     year = {2021},
     doi = {10.5802/crmath.211},
     language = {en},
}

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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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