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 \({\mathbb {R}^k.}\)
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R. Urban was supported in part by the MNiSW research grant N N201 393937.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Penney, R., Urban, R. Estimates for the Poisson kernel and the evolution kernel on the Heisenberg group. J. Evol. Equ. 12, 327–351 (2012). https://doi.org/10.1007/s00028-011-0134-y
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DOI: https://doi.org/10.1007/s00028-011-0134-y