JACOBI TRANSFORM OF \((\nu, \gamma, p)\)-JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE \(\mathrm{L}^{p}(\mathbb{R}^{+},\Delta_{(\alpha,\beta)}(t) dt)\)

Abstract

Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions , Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the \((\nu, \gamma, p)\)-Jacobi–Lipschitz class in the space \(\mathrm{L}^{p}(\mathbb{R}^{+},\Delta_{(\alpha,\beta)}(t)dt)\).