In this paper we introduce a new atomic Hardy space X1(γ) adapted to
the Gauss measure γ, and prove the boundedness of the first order Riesz
transform associated with the Ornstein-Uhlenbeck operator from X1(γ) to
L1(γ). We also provide a new, short and almost self-contained proof of
its weak-type (1,1).Comment: 16 page