Transition Density Estimates for a Class of Lévy and?Lévy-Type Processes

We show on- and off-diagonal upper estimates for the transition densities of symmetric Lévy and Lévy-type processes. To get the on-diagonal estimates, we prove a Nash-type inequality for the related Dirichlet form. For the off-diagonal estimates, we assume that the characteristic function of a Lévy(-type) process is analytic, which allows us to apply the complex analysis technique.