Lipschitz and BMO norm inequalities for operators

DOI10.1016/J.NA.2009.05.032zbMath1239.42021OpenAlexW2028278595MaRDI QIDQ425822

Shusen Ding

Publication date: 9 June 2012

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.2009.05.032

zbMATH Keywords

operatorsinequalitiesdifferential formsA-harmonic equations

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (11)

Inequalities for the fractional convolution operator on differential forms ⋮ BMO and Lipschitz norm estimates for the composition of Green's operator and the potential operator ⋮ Imbedding theorems in Orlicz-Sobolev space of differential forms ⋮ Recent advances in \(L^p\)-theory of homotopy operator on differential forms ⋮ Estimates for Lipschitz and BMO norms of operators on differential forms ⋮ Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms ⋮ Hardy-Littlewood and Caccioppoli-type inequalities for \(A\)-harmonic tensors ⋮ Local regularity and local boundedness results for very weak solutions of obstacle problems ⋮ Some estimates of integrals with a composition operator ⋮ Estimates for \(L^\varphi \)-Lipschitz and \(L^\varphi \)-BMO norms of differential forms ⋮ Boundedness characterization of composite operator with Orlicz-Lipschitz norm and Orlicz-BMO norm

Cites Work

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• Two-weight imbedding inequalities for solutions to the \(A\)-harmonic equation
• Hardy-Littlewood theorems for \(A\)-harmonic tensors
• Integral estimates for null Lagrangians
• \(A_{r} (\lambda)\)-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
• Weighted Poincaré inequalities for solutions to \(A\)-harmonic equations.
• \(A_{r}^{\lambda}(\Omega)\)-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

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