JournalsrmiVol. 26, No. 2pp. 481–528

Riesz transforms on forms and LpL^p-Hodge decomposition on complete Riemannian manifolds

  • Xiang-Dong Li

    Chinese Academy of Sciences, Beijing, China
Riesz transforms on forms and $L^p$-Hodge decomposition on complete Riemannian manifolds cover
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Abstract

In this paper we prove the Strong LpL^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 LpL^p-norm of the Riesz transforms on forms on complete Riemannian manifolds with suitable curvature conditions. Moreover, we establish the Weak LpL^p-Hodge decomposition theorem on complete Riemannian manifolds with non-negative Weitzenböck curvature.

Cite this article

Xiang-Dong Li, Riesz transforms on forms and LpL^p-Hodge decomposition on complete Riemannian manifolds. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 481–528

DOI 10.4171/RMI/607