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

Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie

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.

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

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