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Estimates for the mixed derivatives of the Green functions on homogeneous manifolds of negative curvature

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Author(s): Roman Urban

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2004;
Issue: 145;
Start page: 1;
Date: 2004;
Original page

Keywords: Green function | second-order differential operators | NA groups | Bessel process | evolutions on nilpotent Lie groups.

ABSTRACT
We consider the Green functions for second-order left-invariant differential operators on homogeneous manifolds of negative curvature, being a semi-direct product of a nilpotent Lie group $N$ and $A=mathbb{R}^+$. We obtain estimates for mixed derivatives of the Green functions both in the coercive and non-coercive case. The current paper completes the previous results obtained by the author in a series of papers [14,15,16,19].
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