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

Abstract

ABSTRACT 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 , . For this purpose, we use a generalized translation operator defined by Flensted-Jensen and Koornwinder.