Riesz transform on manifolds and heat kernel regularity

Pascal Auscher; Thierry Coulhon; Xuan Thinh Duong; Steve Hofmann

Displaying similar documents to “Riesz transform on manifolds and heat kernel regularity”

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.

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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Riesz transforms on connected sums

Gilles Carron (2007)

Annales de l’institut Fourier

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Assume that $M_{0}$ is a complete Riemannian manifold with Ricci curvature bounded from below and that $M_{0}$ satisfies a Sobolev inequality of dimension $ν > 3$ . Let $M$ be a complete Riemannian manifold isometric at infinity to $M_{0}$ and let $p \in (ν / (ν - 1), ν)$ . The boundedness of the Riesz transform of $L^{p} (M_{0})$ then implies the boundedness of the Riesz transform of $L^{p} (M)$

Heat kernel upper bounds on a complete non-compact manifold.

Alexander Grigor'yan (1994)

Revista Matemática Iberoamericana

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Let M be a smooth connected non-compact geodesically complete Riemannian manifold, Δ denote the Laplace operator associated with the Riemannian metric, n ≥ 2 be the dimension of M. Consider the heat equation on the manifold u_t - Δu = 0, where u = u(x,t), x ∈ M, t > 0. The heat kernel p(x,y,t) is by definition the smallest positive fundamental solution to the heat equation which exists on any manifold (see [Ch],...

Harnack inequalities on a manifold with positive or negative Ricci curvature.

Dominique Bakry, Zhongmin M. Qian (1999)

Revista Matemática Iberoamericana

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Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below.

Weak-type estimates for the Riesz transforms associated with the Gaussian measure.

Eugene B. Fabes, Chritian E. Gutiérrez, Roberto Scotto (1994)

Revista Matemática Iberoamericana

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In this paper we will study the behavior of the Riesz transform associated with the Gaussian measure γ(x)dx = edx in the space L (R).