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

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-cont...

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Bibliographic Details
Main Author Bruno, Tommaso
Format Journal Article
LanguageEnglish
Published 22.01.2018
Subjects
Mathematics - Functional Analysis
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Summary: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 $(1,1)$.
DOI:10.48550/arxiv.1801.07214