Abstract
Let S be a semi direct product \(S=N\rtimes A\) where N is a connected and simply connected nilpotent Lie group and A is isomorphic with ℝk, k > 1. We obtain an upper bound for the Poisson kernel for the class of second order left-invariant differential operators on S.
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The second author was supported in part by the MNiSW research grant N N201 393937.
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Penney, R.C., Urban, R. An Upper Bound for the Poisson Kernel on Higher Rank NA Groups. Potential Anal 35, 373–386 (2011). https://doi.org/10.1007/s11118-010-9217-6
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DOI: https://doi.org/10.1007/s11118-010-9217-6
Keywords
- Poisson kernel
- Harmonic functions
- Solvable Lie groups
- Higher rank NA groups
- Homogeneous group
- Left invariant operators
- Brownian motion