Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Boujeddaine, Mustapha; Fahlaoui, Said; Daher, Radouan

doi:10.22075/ijnaa.2015.298

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Document Type : Research Paper

Authors

Mustapha Boujeddaine ¹

Said Fahlaoui ¹

Radouan Daher ²

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

10.22075/ijnaa.2015.298

Abstract

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 $L^{p}$.

Keywords

Dini-Lipschitz functions

Jacobi operator

Jacobi transform