Sufficient conditions for the weighted integrability of Fourier–Helgason transforms in the \(L^{p}\)-space on Damek–Ricci spaces

Abstract

In this paper, we give sufficient conditions for functions defined on the \(L^{p}\)-space on Damek–Ricci spaces, \(1<p\le 2\), providing the weighted integrability of their Fourier–Helgason transforms. These results generalize a famous Titchmarsh’s theorem and Younis’ theorem, due to El Ouadih and Daher on Damek–Ricci spaces (El Ouadih and Daher in L C R Math Acad Sci Paris 359:675–685, 2021).