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

Published 17 Apr 2023 in math.FA | (2304.08554v2)

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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