Counterexamples to the \(L^p\)-Calderón-Zygmund estimate on open manifolds

DOI10.1007/s10455-019-09688-3zbMath1433.58020arXiv1902.10913OpenAlexW2973539858WikidataQ124837957 ScholiaQ124837957MaRDI QIDQ2291465

Siran Li

Publication date: 31 January 2020

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.10913

zbMATH Keywords

Riemannian manifoldHessiancounterexamplewarped productCalderón-Zygmund estimateLaplace-Beltramiopen manifold

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Green's functions for elliptic equations (35J08)

Related Items (8)

Generalized Ornstein-Uhlenbeck semigroups in weighted \(L^p\)-spaces on Riemannian manifolds ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ Some functional properties on Cartan-Hadamard manifolds of very negative curvature ⋮ Sobolev functions without compactly supported approximations ⋮ The behavior of harmonic functions at singular points of \(\mathsf{RCD}\) spaces ⋮ The \(L^p\)-Calderón-Zygmund inequality on non-compact manifolds of positive curvature ⋮ Density and non-density of \(C_c^\infty\hookrightarrow W^{k,p}\) on complete manifolds with curvature bounds ⋮ Higher order distance-like functions and Sobolev spaces

Cites Work

• Curvature estimates for immersed hypersurfaces in Riemannian manifolds
• \(L^ p\)-estimates on functions of the Laplace operator
• A non-inequality for differential operators in the \(L_ 1\) norm
• Analysis of the Laplacian on a complete Riemannian manifold
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Lipschitz maps and nets in Euclidean space
• The Calderón-Zygmund inequality on a compact Riemannian manifold
• Nonlinear Calderón-Zygmund inequalities for maps
• The Calderón-Zygmund inequality and Sobolev spaces on noncompact Riemannian manifolds
• On the existence of certain singular integrals
• Density Problems for second order Sobolev Spaces and Cut-off Functions on Manifolds With Unbounded Geometry
• Unnamed Item

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