On Hardy spaces associated with certain Schrödinger operators in dimension 2

. We study the Hardy space H associated with the Schrödinger operator L = −Δ + V on R, where V ≥ 0 is a compactly supported nonzero C-potential. We prove that this space, which is originally defined by means of the maximal function associated with the semigroup generated by −L, admits a special atomic decomposition with atoms satisfying a weighted cancellation condition with a weight of logarithmic growth.