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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18755 |
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| _version_ | 1866915787814469632 |
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| author | Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| author_facet | Casarino, Valentina Ciatti, Paolo Sjögren, Peter |
| contents | We prove that the jump quasi-seminorm of order $\varrho= 2$ for a general Ornstein--Uhlenbeck semigroup $\left(\mathcal H_t\right)_{t>0}$ in $\mathbb R^n$ defines an operator of weak type $(1,1)$ with respect to the invariant measure. This provides an example of a weak-type jump inequality for a nonsymmetric semigroup in a nondoubling measure space.
Our result may be seen as an endpoint refinement of the weak type $(1,1)$ inequality for the $\varrho$-th order variation seminorm of $\left(\mathcal H_t\right)_{t>0}$, recently proved by the authors when $\varrho>2$, and disproved for $\varrho=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18755 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak type (1,1) jump inequalities in a nonsymmetric Gaussian setting Casarino, Valentina Ciatti, Paolo Sjögren, Peter Functional Analysis 37A46, 37A30, 47D03, 42B99 We prove that the jump quasi-seminorm of order $\varrho= 2$ for a general Ornstein--Uhlenbeck semigroup $\left(\mathcal H_t\right)_{t>0}$ in $\mathbb R^n$ defines an operator of weak type $(1,1)$ with respect to the invariant measure. This provides an example of a weak-type jump inequality for a nonsymmetric semigroup in a nondoubling measure space. Our result may be seen as an endpoint refinement of the weak type $(1,1)$ inequality for the $\varrho$-th order variation seminorm of $\left(\mathcal H_t\right)_{t>0}$, recently proved by the authors when $\varrho>2$, and disproved for $\varrho=2$. |
| title | Weak type (1,1) jump inequalities in a nonsymmetric Gaussian setting |
| topic | Functional Analysis 37A46, 37A30, 47D03, 42B99 |
| url | https://arxiv.org/abs/2510.18755 |