  We study Hardy spaces for Fourier--Bessel expansions associated with Bessel
operators on $((0,1), x^{2\nu+1}\, dx)$ and $((0,1), dx)$. We define Hardy
spaces $H^1$ as the sets of $L^1$-functions for which their maximal functions
for the corresponding Poisson semigroups belong to $L^1$. Atomic
characterizations are obtained.
