On the variation operator for the Ornstein–Uhlenbeck semigroup in dimension one
Journal article, 2024
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.
Mehler kernel
Ornstein–Uhlenbeck semigroup
Variation seminorm
Author
VALENTINA CASARINO
University of Padua
PAOLO CIATTI
University of Padua
Peter Sjögren
Chalmers, Mathematical Sciences
University of Gothenburg
Annali di Matematica Pura ed Applicata
0373-3114 (ISSN) 1618-1891 (eISSN)
Vol. 203 205-219Subject Categories (SSIF 2011)
Algebra and Logic
Computational Mathematics
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1007/s10231-023-01358-3