Generalized Fourier–Bessel transform of \(2\textit{pq}\)-Bessel–Lipschitz functions with higher order difference

Let \(n\in \mathbb {N}\) $n\in \mathbb{N}$ and \(\alpha >\frac{-1}{2}\) $\alpha >\frac{-1}{2}$ . The purpose of the present work is to show an analogue of a classic Titchmarsh theorem to higher differences of functions belonging to \(L_{\alpha ,n}^{p} ( \mathbb {R}^{+})\) $L_{\alpha ,n}^p({\mathbb{R}}^{+})$ where \(1<p\le 2 \) $1<p\le 2$ .