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arXiv · 2304.08554

On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one

Valentina Casarino·Paolo Ciatti·Peter Sjögren
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Abstract

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.

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Valentina Casarino, Paolo Ciatti, Peter Sjögren. 2023-04-17. On the variation operator for the Ornstein-Uhlenbeck semigroup in dimension one. https://arxiv.org/abs/2304.08554

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