Consider the variation seminorm of the Ornstein–Uhlenbeck semigroup Ht 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 Lp estimates for 1 < p< ∞ were already known.
On the variation operator for the Ornstein–Uhlenbeck semigroup in dimension one
Valentina Casarino
Membro del Collaboration Group
;Paolo CiattiMembro del Collaboration Group
;
2024
Abstract
Consider the variation seminorm of the Ornstein–Uhlenbeck semigroup Ht 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 Lp estimates for 1 < p< ∞ were already known.
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