Characterization of Dini Lipschitz Functions in Terms of Their Helgason Transform

In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [6] for the Helgason Fourier transform of a set of functions satisfying the Dini Lipschitz condition in the space L² for functions on noncompact rank one Riemannian symmetric spaces.