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<∞ 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
;
2023
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<∞ were already known.File in questo prodotto:
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