Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds

Steve Hofmann, Marius Mitrea, Sylvie Monniaux

Type: Article

Publication Date: 2011-01-01

Citations: 7

DOI: https://doi.org/10.5802/aif.2642

Abstract

We prove L p -bounds for the Riesz transforms associated to the Hodge-Laplacian equipped with absolute and relative boundary conditions in a Lipschitz subdomain of a (smooth) Riemannian manifold for p in a certain interval depending on the Lipschitz character of the domain.

Locations

French digital mathematics library (Numdam) - View - PDF
Annales de l’institut Fourier - View - PDF

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+	Semigroups of Linear Operators and Applications to Partial Differential Equations	1983	A. Pazy
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+ PDF Chat	A T(b) theorem with remarks on analytic capacity and the Cauchy integral	1990	Michael Christ
+	The Inhomogeneous Dirichlet Problem in Lipschitz Domains	1995	David Jerison Carlos E. Kenig
+ PDF Chat	Calderón-Zygmund theory for non-integral operators and the $H^{\infty}$ functional calculus	2003	Sönke Blunck Peer Christian Kunstmann
+	Sharp Hodge decompositions, Maxwell's equations, and vector Poisson problems on nonsmooth, three-dimensional Riemannian manifolds	2004	Marius Mitrea
+ PDF Chat	$L^p$ bounds for Riesz transforms and square roots associated to second order elliptic operators	2003	Steve Hofmann José María Martell
+	On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds	2008	Marius Mitrea Sylvie Monniaux