Endpoint results for the Riesz transform of the Ornstein-Uhlenbeck operator

الأصل · EN

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).