The aim of this paper is to prove a generalization of Titchmarsh’s theorems for the generalized Fourier transform called (
κ
,
n
{\kappa,n}
)-Fourier transform, where n is a positive integer and κ is a constant coming from Dunkl theory. As an application, we derive a
(
κ
,
n
)
{(\kappa,n)}
-Fourier multiplier theorem for
L
2
{L^{2}}
Lipschitz spaces. Moreover, we give necessary conditions to ensure that f belongs to either one of the generalized Lipschitz classes of order m. This allows us to establish the analogue of the Boas-type result for
ℱ
κ
,
n
{\mathcal{F}_{\kappa,n}}
.