Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 145, pp. 1-10.

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

Author: Roman Urban (Univ. of Wroclaw, Poland)

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].

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.