ESTIMATES FOR THE POISSON KERNELS ON HOMOGENEOUS
MANIFOLDS OF NEGATIVE CURVATURE AND THE BOUNDARY
HARNACK INEQUALITY IN THE NONCOERCIVE CASE
Abstract: 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.
1991 AMS Mathematics Subject Classification: 22E25, 43A85, 53C30, 31B25.
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