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).
Endpoint Results for the Riesz Transform of the Ornstein–Uhlenbeck Operator
Bruno T.
2019-01-01
Abstract
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).
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