  We consider an infinite homogeneous tree V endowed with the usual metric d
defined on graphs and a weighted measure \mu. The metric measure space V,d,\mu)
is nondoubling and of exponential growth, hence the classical theory of Hardy
spaces does not apply in this setting. We construct an atomic Hardy space H^1
on (V,d,\mu) and investigate some of its properties, focusing in particular on
real interpolation properties and on boundedness of singular integrals on H^1.
