Lp identities and inequalities related to certain Levy proceses

I will present recent results, concerned with generators and forms (acting on Lp) related to Levy processes. We establish the Hardy-Stein identity in Lp and related multivariate identities. If time permits, we will also present the optimal Hardy inequality for stable processes. All these results require the Lp-counterpart of the usual Dirichlet form of the process, which will be introduced beforehand.