We prove -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 in a certain interval depending on the Lipschitz character of the domain.
Nous prouvons des estimations 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 dans un intervalle dépendant des constantes lipschitziennes du domaine.
Keywords: Hodge-Laplacian, Riesz transforms, differential forms, Lipschitz domain, Riemannian manifolds
Mot clés : Laplacien de Hodge, transformées de Riesz, formes différentielles, domaines lipschitziens
@article{AIF_2011__61_4_1323_0, author = {Hofmann, Steve and Mitrea, Marius and Monniaux, Sylvie}, title = {Riesz transforms associated with the {Hodge} {Laplacian} in {Lipschitz} subdomains of {Riemannian} manifolds}, journal = {Annales de l'Institut Fourier}, pages = {1323--1349}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {4}, year = {2011}, doi = {10.5802/aif.2642}, zbl = {1239.42013}, mrnumber = {2951495}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2642/} }
TY - JOUR AU - Hofmann, Steve AU - Mitrea, Marius AU - Monniaux, Sylvie TI - Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds JO - Annales de l'Institut Fourier PY - 2011 SP - 1323 EP - 1349 VL - 61 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2642/ DO - 10.5802/aif.2642 LA - en ID - AIF_2011__61_4_1323_0 ER -
%0 Journal Article %A Hofmann, Steve %A Mitrea, Marius %A Monniaux, Sylvie %T Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds %J Annales de l'Institut Fourier %D 2011 %P 1323-1349 %V 61 %N 4 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2642/ %R 10.5802/aif.2642 %G en %F AIF_2011__61_4_1323_0
Hofmann, Steve; Mitrea, Marius; Monniaux, Sylvie. Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds. Annales de l'Institut Fourier, Volume 61 (2011) no. 4, pp. 1323-1349. doi : 10.5802/aif.2642. http://www.numdam.org/articles/10.5802/aif.2642/
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