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arXiv · 1801.07214

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

Tommaso Bruno
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Abstract

In this paper we introduce a new atomic Hardy space $X^1(\gamma)$ adapted to the Gauss measure $\gamma$, and prove the boundedness of the first order Riesz transform associated with the Ornstein-Uhlenbeck operator from $X^1(\gamma)$ to $L^1(\gamma)$. We also provide a new, short and almost self-contained proof of its weak-type $(1,1)$.

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Tommaso Bruno. 2018-01-22. Endpoint results for the Riesz transform of the Ornstein-Uhlenbeck operator. https://arxiv.org/abs/1801.07214

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