Titchmarsh theorem for Jacobi Dini-Lipshitz functions

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}^{+}), (۱< p\leq ۲). 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