Endpoint Results for the Riesz Transform of the Ornstein–Uhlenbeck Operator

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

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Bibliographic Details
Published inThe Journal of fourier analysis and applications Vol. 25; no. 4; pp. 1609 - 1631
Main Author Bruno, Tommaso
Format Journal Article
LanguageEnglish
Published New York Springer US 15.08.2019
Springer
Springer Nature B.V
Subjects
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal,Image and Speech Processing
Riesz transforms
Ornstein–Uhlenbeck
42B25
42B30
Weak type
42B20
Endpoint result
Hardy space
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Summary:In this paper we introduce a new atomic Hardy space X 1 ( γ ) adapted to the Gauss measure γ , and prove the boundedness of the first order Riesz transform associated with the Ornstein–Uhlenbeck operator from X 1 ( γ ) to L 1 ( γ ) . We also provide a new, short and almost self-contained proof of its weak-type (1, 1).
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-018-09648-8