Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Document Type : Research Paper


1 Department of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d Analyse Harmonique et Probabilies, Universite Moulay Ismail, BP 11201 Zitoune, Meknes, Morocco

2 Department of Mathematics, Faculty of Sciences An Chock, University of Hassan II, BP 5366, Maarif, Casablanca, Morocco


Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $\mathrm{L}_{(\alpha,\beta)}^{p}(\mathbb{R}^{+})$, $(1< p\leq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lipschitz condition in $L^{p}$.