An analog of Titchmarsh's theorem for the Bessel transform in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$

Abstract

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1<pleq 2$.