no. 4
Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds
[Estimations L p pour les transformées de Riesz associées au Laplacien de Hodge dans des domaines lipschitziens de variétés riemanniennes]
Hofmann, Steve1 ; Mitrea, Marius1 ; Monniaux, Sylvie2
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)
Annales de l'Institut Fourier, Tome 61 (2011) no. 4, pp. 1323-1349.

Nous prouvons des estimations L p 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 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.

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://aif.centre-mersenne.org/articles/10.5802/aif.2642/

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