Pointwise estimates for the Poisson kernel on \(NA\) groups by the Ancona method

DOI10.5802/afst.834zbMath0876.22008OpenAlexW2326740292MaRDI QIDQ1355485

Ewa Damek

Publication date: 5 November 1997

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1996_6_5_3_421_0

zbMATH Keywords

Martin boundaryPoisson kernelsubelliptic operators\(NA\) groups

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Nilpotent and solvable Lie groups (22E25)

Cites Work

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• Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel
• Negatively curved manifolds, elliptic operators, and the Martin boundary
• Harmonic analysis on solvable extensions of H-type groups
• On homogeneous manifolds of negative curvature
• Principe du maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérées
• Les fonctions surharmoniques dans l'axiomatique de Monsieur Brelot associées à un opérateur elliptique dégénéré. (Superharmonic functions in the axiomatics of Monsieur Brelot associated with a degenerate elliptic operator)
• Boundaries for left-invariant sub-elliptic operators on semidirect products of nilpotent and abelian groups.
• Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups
• The Fatou theorem for NA groups - a negative result
• Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
• Brownian motion in certain symmetric spaces and nonnegative eigenfunctions of the Laplace-Beltrami operator

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