Valentina Casarino

Sharp variational, jump and oscillation bounds in a general Gaussian context

We consider a general, nonsymmetric Ornstein--Uhlenbeck semigroup $(\mathcal H_t)_{t>0}$. We prove an $L^p$ bound for the jump quasi-seminorms for $1<p<\infty$ and a weak type (1,1) oscillation inequality, both with respect to the invariant measure. These results are established for the order $\varrho=2$. To do so, we...