Geodesic
Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature
Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 1 
R. Urban. Estimates for derivatives of the Green functions on homogeneous manifolds
of negative curvature. Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a3/
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     title = {Estimates for derivatives of the {Green} functions on homogeneous manifolds
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     year = {2004},
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     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a3/}
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Voir la notice de l'article provenant de la source Comenius University

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. Download: Adobe PDF Compressed Postscript Version to read: Adobe PDF Acta Mathematica Universitatis Comenianae Institute of Applied Mathematics Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295755 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © Copyright 2004, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE