Norms of the composition of the maximal and projection operators

DOI10.1016/J.NA.2010.02.038zbMATH Open1189.35036OpenAlexW2088653835MaRDI QIDQ972414

Shusen Ding, Yuming Xing

Publication date: 25 May 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.02.038

zbMATH Keywords

differential formsharmonic equations

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Implicit function theorems, Jacobians, transformations with several variables (26B10) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Other generalizations (nonlinear potential theory, etc.) (31C45)

Cites Work

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• Two-weight imbedding inequalities for solutions to the \(A\)-harmonic equation
• Global weighted inequalities for operators and harmonic forms on manifolds
• Norm comparison inequalities for the composite operator
• Hardy-Littlewood theorems for \(A\)-harmonic tensors
• Integral estimates for null Lagrangians
• Global integrability theorems for \(A\)-harmonic tensors
• \(A_{r} (\lambda)\)-weighted Caccioppoli-type and Poincaré-type inequalities for \(A\)-harmonic tensors
• Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
• Weak reverse Hölder inequalities and imbedding inequalities for solutions to 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

Related Items (5)

Existence of solutions for nonhomogeneous \(A\)-harmonic equations with variable growth ⋮ Norm comparison estimates for the composite operator ⋮ Recent advances in \(L^p\)-theory of homotopy operator on differential forms ⋮ Poincaré-type inequalities for the composite operator in \(L^{\mathcal{A}}\)-averaging domains ⋮ Some higher norm inequalities for composition of power operators

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