  In this paper we prove the Fourier restriction theorem for $p=2$ on
Riemannian symmetric spaces of noncompact type with real rank one which extends
the earlier result proved in \cite[Theorem 1.1]{KRS}. This result depends on
the weak $L^2$ estimates of the Poisson transform of $L^2$ function. By using
this estimate of the Poisson transform we also characterizes all weak $L^2$
eigenfunction of the Laplace--Beltrami operator of Riemannian symmetric spaces
of noncompact type with real rank one and eigenvalue $-(\lambda^2+\rho^2)$ for
$\lambda\in\R\setminus\{0\}$.
