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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.18755 |
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Table of 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 $\varrho=2$.