  Let $\lambda>0$, $p\in((2\lz+1)/(2\lz+2), 1]$, and
$\triangle_\lambda\equiv-\frac{d^2}{dx^2}-\frac{2\lambda}{x} \frac d{dx}$ be
the Bessel operator. In this paper, the authors establish the characterizations
of atomic Hardy spaces $H^p((0, \infty), dm_\lambda)$ associated with
$\triangle_\lambda$ in terms of the radial maximal function, the nontangential
maximal function, the grand maximal function, the Littlewood-Paley $g$-function
and the Lusin-area function, where $dm_\lambda(x)\equiv x^{2\lambda}\,dx$. As
an application, the authors further obtain the Riesz transform characterization
of these Hardy spaces.
