|
|||||
|
|
Estimates for the Poisson kernel and the evolution kernel on the Heisenberg group |
|
| Authors: | Richard Penney Roman Urban |
| Affiliation: | 1. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA 2. Institute of Mathematics, Wroclaw University, Plac Grunwaldzki 2/4, 50-384, Wroclaw, Poland |
| Abstract: | We 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 ${A = mathbb {R}^k.}$ We also give an upper estimate for the transition probabilities of the evolution on ${mathcal H_{n}}$ driven by the Brownian motion (with drift) in ${mathbb {R}^k.}$ |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |