Endpoint estimates for higher order Gaussian Riesz transforms
| Autor: | Berra, Fabio, Dalmasso, Estefanía, Scotto, Roberto |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We will show that, contrary to the behavior of the higher order Riesz transforms studied so far on the atomic Hardy space $\mathcal{H}^1(\mathbb R^n, \gamma)$, associated with the Ornstein-Uhlenbeck operator with respect to the $n$-dimensional Gaussian measure $\gamma$, the new Gaussian Riesz transforms are bounded from $\mathcal{H}^1(\mathbb R^n, \gamma)$ to $L^1(\mathbb R^n, \gamma)$, for any order and dimension $n$. We will also prove that the classical Gaussian Riesz transforms of higher order are bounded from an adequate subspace of $\mathcal{H}^1(\mathbb R^n, \gamma)$ into $L^1(\mathbb R^n, \gamma)$, extending Bruno's result (J. Fourier Anal. Appl. 25, 4 (2019), 1609--1631) for the first order case. Comment: 15 pages |
| Databáze: | arXiv |
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