Riesz transforms on forms and $L^p$-Hodge decomposition on complete Riemannian manifolds
Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, p. 481-528 / Harvested from Project Euclid
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In this paper we prove the Strong $L^p$-stability of the heat semigroup generated by the Hodge Laplacian on complete Riemannian manifolds with non-negative Weitzenböck curvature. Based on a probabilistic representation formula, we obtain an explicit upper bound of the $L^p$-norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak $L^p$-Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenböck curvature.
Publié le : 2010-06-15
Classification:  Hodge decomposition,  martingale transforms,  Riesz transforms,  Weitzenböck curvature,  53C21,  58J65,  58J40,  60J65 
@article{1275671309,
     author = {Li
, 
Xiang-Dong},
     title = {Riesz transforms on forms and $L^p$-Hodge decomposition on
complete Riemannian manifolds},
     journal = {Rev. Mat. Iberoamericana},
     volume = {26},
     number = {1},
     year = {2010},
     pages = { 481-528},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1275671309}
}

Li
, 
Xiang-Dong. Riesz transforms on forms and $L^p$-Hodge decomposition on
complete Riemannian manifolds. Rev. Mat. Iberoamericana, Tome 26 (2010) no. 1, pp.  481-528. http://gdmltest.u-ga.fr/item/1275671309/