Journal of Lie Theory 31 (2021), No. 1, 287--300
Copyright Heldermann Verlag 2021
Riesz Potentials for the κ-Generalized Fourier Transform
Sara Oukili
Laboratoire d'Analyse Mathématiques et Applications, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis, Tunisia
oukili2213@gmail.com
Mohamed Sifi
Laboratoire d'Analyse Mathématiques et Applications, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092 Tunis, Tunisia
mohamed.sifi@fst.utm.tn
We investigate the Lp-Lq boundedness properties of the Riesz potentials Iκβ and the fractional maximal function Mκ, β associated with the κ-generalized Fourier transform. As application, we establish a Welland inequality.
Keywords: Generalized Fourier transform, Riesz potentials, fractional maximal function, Welland inequality.
MSC: 42B25; 42B10.
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