Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds
[Estimations Lp pour les transformées de Riesz associées au Laplacien de Hodge dans des domaines lipschitziens de variétés riemanniennes]
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1323-1349.

Nous prouvons des estimations Lp pour les transformées de Riesz associées au Laplacien de Hodge muni de conditions au bord absolues et relatives dans un domaine lipschitzien d’une variété riemannienne (lisse) pour p dans un intervalle dépendant des constantes lipschitziennes du domaine.

We prove Lp-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.

DOI : 10.5802/aif.2642
Classification : 42B20, 58J32, 42B25, 58J05
Keywords: Hodge-Laplacian, Riesz transforms, differential forms, Lipschitz domain, Riemannian manifolds
Mot clés : Laplacien de Hodge, transformées de Riesz, formes différentielles, domaines lipschitziens
Hofmann, Steve 1 ; Mitrea, Marius 1 ; Monniaux, Sylvie 2

1 University of Missouri Department of Mathematics Columbia - 202 Mathematical Sciences Building Columbia, MO 65211 (USA)
2 Université Paul Cézanne LATP - UMR 6632 Faculté des Sciences et Techniques Avenue Escadrille Normandie Niémen 13397 Marseille Cédex 20 (France)
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Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie. Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1323-1349. doi : 10.5802/aif.2642. https://www.numdam.org/articles/10.5802/aif.2642/

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