Tuesday, March 26, 2024 — 11:30 am — Laboratorio Zironi, edificio Matematica
Variational inequalities for the Ornstein-Uhlenbeck semigroup
Abstract: In this talk we introduce variation seminorms and consider the variation operator of the Ornstein-Uhlenbeck semigroup $(H_t)_{t> 0}$, taken with respect to $t$, in $\mathbb R^n$. We prove, by a simple geometric approach, that this seminorm defines an operator of weak type $(1, 1) $ for the relevant Gaussian measure in dimension one. The higher-dimensional case requires a different approach, based, in particular, on vector-valued Calderón–Zygmund theory.
The talk is based on joint work with Paolo Ciatti and Peter Sjögren.