On the strong \(L^p\)-Hodge decomposition over complete Riemannian manifolds

DOI10.1016/j.jfa.2009.08.002zbMath1196.58001OpenAlexW2056158881MaRDI QIDQ1039417

Xiang Dong Li

Publication date: 30 November 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.08.002

zbMATH Keywords

Riesz transformsPoincaré inequalitiesRiesz potentials\(L^p\)-cohomologystrong \(L^p\)-Hodge decomposition

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Hodge theory in global analysis (58A14)

Related Items

Sobolev inequalities on forms and \(L^{p,q}\)-cohomology on complete Riemannian manifolds ⋮ Geometry on the Wasserstein space over a compact Riemannian manifold ⋮ On the \(L^{r}\) Hodge theory in complete non compact Riemannian manifolds ⋮ p-harmonic 1-forms on totally real submanifolds in complex space forms ⋮ The Hölder-Poincaré duality for \(L _{q,p }\)-cohomology ⋮ Variable exponent spaces of differential forms on Riemannian manifold ⋮ \(L^p\)-estimates and existence theorems for the \(\bar \partial\)-operator on complete Kähler manifolds ⋮ Riesz transforms on forms and \(L^p\)-Hodge decomposition on complete Riemannian manifolds ⋮ On the weak \(L ^{p }\)-Hodge decomposition and Beurling--Ahlfors transforms on complete Riemannian manifolds ⋮ Riesz transforms and spectral multipliers of the Hodge-Laguerre operator ⋮ The LIR method. \(L^{r}\) solutions of elliptic equation in a complete Riemannian manifold ⋮ Analysis of the Hodge Laplacian on the Heisenberg group

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