Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms

Ewa Damek

Displaying similar documents to “Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms”

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

Ewa Damek (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

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Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.

Ewa Damek, Andrzej Hulanicki, Roman Urban (2001)

Revista Matemática Iberoamericana

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In this paper we treat noncoercive operators on simply connected manifolds of negative curvature.

Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups

Ewa Damek (1988)

Studia Mathematica

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Riesz means on Lie groups and riemannian manifolds of nonnegative curvature

Georgios Alexopoulos, Noël Lohoué (1994)

Bulletin de la Société Mathématique de France

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Estimates for the Poisson kernels and their derivatives on rank one NA groups

Ewa Damek, Andrzej Hulanicki, Jacek Zienkiewicz (1997)

Studia Mathematica

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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.

Rough isometries and p-harmonic functions with finite Dirichlet integral.

Ilkka Holopainen (1994)

Revista Matemática Iberoamericana

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A Paley-Wiener theorem on NA harmonic spaces

Francesca Astengo, Bianca di Blasio (1999)

Colloquium Mathematicae

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Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.

Riesz transform on manifolds and Poincaré inequalitie

Pascal Auscher, Thierry Coulhon (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We study the validity of the $L^{p}$ inequality for the Riesz transform when $p > 2$ and of its reverse inequality when $1 < p < 2$ on complete riemannian manifolds under the doubling property and some Poincaré inequalities.