A remark on the Poisson kernels on homogeneous manifolds of negative curvature

• Autorzy: Urban A.
• Języki publikacji: EN

Abstrakty

EN

In this note we give an improvement of the estimate of the Poisson kernels for second order differential operators on homogeneous manifolds of negative curvature obtained for the first time, using some probabilistic techniques, in [1] and then improved by the author in [4].

Słowa kluczowe

EN

Poisson kernels; differential operators; homogeneous manifold

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 2
• Strony: 289--291
• Opis fizyczny: Biblogr. 4 poz.

Twórcy

autor

Urban A.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] E. Damek, A. Hulanicki and R. Urban, Martin boundary for homogeneous Riemannian manifolds of negative curvature at the bottom of the spectrum, Rev. Mat. Iberoamericana 17 (2) (2001), pp. 257-293.
• [2] L. Élie, Comportement asymptotique du noyau potentiel sur les groupes de Lie, Ann. Scient. École Norm. Sup. 4 (1982), pp. 257-364.
• [3] E. Heintze, On homogeneous manifolds of negative curvature, Math. Ann. 211 (1974), pp. 23-34.
• [4] R. Urban, Estimates for the Poisson kernels on homogeneous manifolds of negative curvature and the boundary Hamack inequality in the noncoercive case, Probab. Math. Statist. 21 (1) (2001), pp. 213-229.