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

Tommaso Bruno (UGent)
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Abstract
In this paper we introduce a new atomic Hardy space X1(gamma) adapted to the Gauss measure gamma, and prove the boundedness of the first order Riesz transform associated with the Ornstein-Uhlenbeck operator from X1(gamma) to L1(gamma). We also provide a new, short and almost self-contained proof of its weak-type (1,1).
Keywords
Riesz transforms, Ornstein-Uhlenbeck, Hardy space, Weak type, Endpoint result, HARDY-TYPE SPACES, H-1, BMO

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MLA
Bruno, Tommaso. “Endpoint Results for the Riesz Transform of the Ornstein–Uhlenbeck Operator.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, no. 4, 2019, pp. 1609–31, doi:10.1007/s00041-018-09648-8.
APA
Bruno, T. (2019). Endpoint results for the Riesz transform of the Ornstein–Uhlenbeck operator. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(4), 1609–1631. https://doi.org/10.1007/s00041-018-09648-8
Chicago author-date
Bruno, Tommaso. 2019. “Endpoint Results for the Riesz Transform of the Ornstein–Uhlenbeck Operator.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25 (4): 1609–31. https://doi.org/10.1007/s00041-018-09648-8.
Chicago author-date (all authors)
Bruno, Tommaso. 2019. “Endpoint Results for the Riesz Transform of the Ornstein–Uhlenbeck Operator.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25 (4): 1609–1631. doi:10.1007/s00041-018-09648-8.
Vancouver
1.
Bruno T. Endpoint results for the Riesz transform of the Ornstein–Uhlenbeck operator. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2019;25(4):1609–31.
IEEE
[1]
T. Bruno, “Endpoint results for the Riesz transform of the Ornstein–Uhlenbeck operator,” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, no. 4, pp. 1609–1631, 2019.
@article{8663741,
  abstract     = {{In this paper we introduce a new atomic Hardy space X1(gamma) adapted to the Gauss measure gamma, and prove the boundedness of the first order Riesz transform associated with the Ornstein-Uhlenbeck operator from X1(gamma) to L1(gamma). We also provide a new, short and almost self-contained proof of its weak-type (1,1).}},
  author       = {{Bruno, Tommaso}},
  issn         = {{1069-5869}},
  journal      = {{JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS}},
  keywords     = {{Riesz transforms,Ornstein-Uhlenbeck,Hardy space,Weak type,Endpoint result,HARDY-TYPE SPACES,H-1,BMO}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1609--1631}},
  title        = {{Endpoint results for the Riesz transform of the Ornstein–Uhlenbeck operator}},
  url          = {{http://dx.doi.org/10.1007/s00041-018-09648-8}},
  volume       = {{25}},
  year         = {{2019}},
}

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