Estimates for the Poisson kernel and the evolution kernel on the Heisenberg group (Q692818)

The authors obtain an upper estimate for the Poisson kernel for the class of second order left invariant differential operators on the semi-direct product of the \(2n+1\)-dimensional Heisenberg group \({\mathcal H}_n\) and an Abelian group \(R^k\). Besides, an upper estimate for the transition probabilities of the evolution on \({\mathcal H}_n\) driven by the Brownian motion with drift in \(R^k\), is given.