Singular integrals of the compositions of Laplace-Beltrami and Green's operators

DOI10.1186/1029-242X-2011-74zbMath1277.58003OpenAlexW2108597584WikidataQ59270069 ScholiaQ59270069MaRDI QIDQ357348

Shusen Ding, Ru Fang

Publication date: 30 July 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2011-74

zbMATH Keywords

differential formsLaplace-Beltrami operatorPoincaré-type inequalitiesGreen's operator\(A\)-harmonic equations

Mathematics Subject Classification ID

Exterior differential systems (Cartan theory) (58A15) Inequalities involving derivatives and differential and integral operators (26D10) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (3)

Higher integrability of iterated operators on differential forms ⋮ Green’s Operator and Differential Forms ⋮ Imbedding inequalities with \(L{\varphi}\)-norms for composite operators

Cites Work

• Two-weight imbedding inequalities for solutions to the \(A\)-harmonic equation
• Global weighted inequalities for operators and harmonic forms on manifolds
• A singular integral of the composite operator
• Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
• \(L^{\varphi}(\mu)\)-averaging domains and the quasi-hyperbolic metric
• \(A_{r}^{\lambda}(\Omega)\)-weighted imbedding inequalities for \(A\)-harmonic tensors.
• Weighted integral inequalities for solutions of the \(A\)-harmonic equation
• Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds
• L p Theory of Differential Forms on Manifolds

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