Integrability of the Fourier-Jacobi transform of functions satisfying Lipschitz and Dini-Lipschitz-type estimates

The purpose of this work is to prove analogues of the classical Titchmarsh theorem and Younis' theorem associated with the Fourier-Jacobi transform of a set of functions satisfying a generalized Lipschitz condition of a certain order in suitable weighted spaces L-p([0,+infinity)), 1 < p <= 2. For this purpose, we use a generalized translation operator defined by Flensted-Jensen and Koornwinder.