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Estimates for the Poisson kernels on homogeneous manifolds of negative curvature and the boundary Harnack inequality in the noncoercive case

Urban R.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 1

213--229

Using a probabilistic technique we obtain upper and lower estimates for the Poisson kernels of the second order differential operators on a homogeneous manifold of negative curvature. Our results improve estimates obtained in the paper [5]. Moreover, for the noncoercive operator we proved the boundary Harnack inequality which turned out to be the same as in the coercive case.