Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for the Poisson kernels and their derivatives on rank one NA groups
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.
Estimates of Green functions and their applications for parabolic operators with singular potentials
We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.