On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866910429566992384 |
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| author | Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| author_facet | Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| contents | Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup $H_t$ in dimension one, taken with respect to $t$. We show that this seminorm defines an operator of weak type $(1,1)$ for the relevant Gaussian measure. The analogous $L^p$ estimates for $1<p<\infty$ were already known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_08554 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one Casarino, Valentina Ciatti, Paolo Sjögren, Peter Functional Analysis 42A99, 47D03 Consider the variation seminorm of the Ornstein-Uhlenbeck semigroup $H_t$ in dimension one, taken with respect to $t$. We show that this seminorm defines an operator of weak type $(1,1)$ for the relevant Gaussian measure. The analogous $L^p$ estimates for $1<p<\infty$ were already known. |
| title | On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one |
| topic | Functional Analysis 42A99, 47D03 |
| url | https://arxiv.org/abs/2304.08554 |