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 and . 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].
Submitted October 17, 2003. Published December 7, 2004.
Math Subject Classifications: 22E25, 43A85, 53C30.
Key Words: Green function; second-order differential operators; NA groups; Bessel process; evolutions on nilpotent Lie groups.
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| Roman Urban |
Institute of Mathematics
University of Wroclaw
Pl. Grunwaldzki 2/4
50-384 Wroclaw, Poland
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