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Estimates for derivatives of the Green functions for the noncoercive differential operators on homogeneous manifolds of negative curvature. II. (English) Zbl 1041.43004
[Part I by the same author in Potential Anal. 19, 317–339 (2003; Zbl 1028.43010).]
The author studies noncoercive operators $$L$$ of the following form $L= \sum^m_{j=1} \phi_a(X_j)^2+ \phi_a(X)+ a^2\partial^2_a+ \partial_a,$ where $$X,X_1,\dots, X_m$$ are left-invariant vector fields on $$N$$; moreover, the vector fields $$X_1,\dots, X_m$$ are linearly independent and generate $$n$$, $\phi_a= \text{Ad}_{\exp(\log a)Y_0}= e^{(\log a)\text{ad\,}Y_0}= e^{(\log a)D},$ where $$D= \text{ad}_{Y_0}$$ is a derivation of the Lie algebra $$n$$ of the Lie group $$N$$ such that the real parts $$d_j$$ of the eigenvalues $$\lambda_j$$ of $$D$$ are positive. The main goal of the paper is to prove estimates for the derivatives of the Green function for $$L$$.
##### MSC:
 43A85 Harmonic analysis on homogeneous spaces 53C30 Differential geometry of homogeneous manifolds
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