Fourier-Bessel transforms of Dini-Lipschitz functions on Lebesgue spaces $L_{p,\gamma}(\mathbb{R}^{n}_{+})$

Abstract

In this paper, we prove a generalization of Titchmarsh's theorem for the Laplace-Bessel differential operator in the space $L_{p,\gamma}(\mathbb{R}^{n}_{+})$ for functions satisfying the $(\psi,p)$-Laplace-Bessel Lipschitz condition for $10 $.