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, Steve ; Mitrea, Marius ; Monniaux, Sylvie

Annales de l'Institut Fourier, Tome 61 (2011), p. 1323-1349 / Harvested from Numdam

Résumé

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.

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.

Détail

Publié le : 2011-01-01

MR 2951495 | Zbl 1239.42013

DOI : https://doi.org/10.5802/aif.2642
Classification:  42B20,  58J32,  42B25,  58J05
Mots clés: Laplacien de Hodge, transformées de Riesz, formes différentielles, domaines lipschitziens

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