Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds
Annales de l'Institut Fourier, Volume 61 (2011) no. 4, p. 1323-1349

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.

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.

DOI : https://doi.org/10.5802/aif.2642
Classification:  42B20,  58J32,  42B25,  58J05
Keywords: Hodge-Laplacian, Riesz transforms, differential forms, Lipschitz domain, Riemannian manifolds
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {4},
     year = {2011},
     pages = {1323-1349},
     doi = {10.5802/aif.2642},
     mrnumber = {2951495},
     zbl = {1239.42013},
     language = {en},
     url = {http://www.numdam.org/item/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/item/AIF_2011__61_4_1323_0/

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