Characterization of $(\eta,\gamma,k,2)$-Dini-Lipschitz functions in terms of their Helgason Fourier transform

Abstract

In this paper, using a generalized translation operator, we obtain an analog ofYounis Theorem 5.2 in [M. S. Younis, Fourier transforms of Dini-Lipschitz functions, Int. J. Math. Math. Sci. 9 (2),(1986), 301–312.]for the Helgason Fourier transform of a set of functions satisfying the $(\eta,\gamma,k,2)$-Dini-Lipschitz condition in the space $L^{2}$for functions on noncompact rank one Riemannian symmetric spaces.