An analog of Titchmarsh's theorem for the Bessel transform in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$

Document Type: Research Paper

Authors

1 Department of Mathematics, Faculty of Sciences A"{i}n Chock, University of Hassan II, BP 5366, Maarif, Casablanca, Morocco

2 Department of Mathematics, Faculty of Sciences A"{i}n Chock, University of Hassan II, BP 5366, Maarif, Casablanca, Morocco

3 Department of Mathematics and Computer Sciences, Faculty of Sciences, Equipe d'Analyse Harmonique et Probabilit'{e}s, Universit'{e} Moulay Isma"{i}l. BP 11201 , Zitoune, Mekn`{e}s, Morocco

Abstract

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $\mathrm{L}_{p,\alpha}(\mathbb{R}_{+})$, where $\alpha>-\frac{1}{2}$ and $1<p\leq 2$.

Keywords