ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIII, 1 (2004)
p. 43 – 53

Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature
R. Urban

Abstract.  We consider the Green functions $\mathcal G$ for second-order coercive differential operators on homogeneous manifolds of negative curvature, being a semi-direct product of a~nilpotent Lie group $N$ and $A=\R^+$.

Estimates for derivatives of the Green functions $\mathcal G$ with respect to the $N$ and $A$-variables are obtained. This paper completes a previous work of the author (see \cite{pota, ejde}) where estimates for derivatives of the Green functions for the noncoercive operators has been obtained. Here we show how to use the previous methods and results from \cite{pota} in order to get analogous estimates for coercive operators.

AMS subject classification:  22E25, 43A85, 53C30, 31B25.
Keywords:  Green function, second-order differential operators, $NA$ groups, Bessel process, evolutions on nilpotent Lie groups.