\(L(\varphi ,\mu )\)-averaging domains and Poincaré inequalities with Orlicz norms

DOI10.1016/j.na.2010.03.018zbMath1202.46033OpenAlexW2053723464MaRDI QIDQ975262

Shusen Ding

Publication date: 9 June 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.2010.03.018

zbMATH Keywords

differential formsPoincaré inequalitiesOrlicz norms\(A\)-harmonic equation

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Nonlinear elliptic equations (35J60) Integration with respect to measures and other set functions (28A25) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (8)

Some Orlicz norms inequalities for the composite operator \(T \circ d \circ H\) ⋮ Some local Poincaré inequalities for the composition of the sharp maximal operator and the Green's operator ⋮ Poincaré inequalities and the sharp maximal inequalities with \(L^{\varphi}\)-norms for differential forms ⋮ Poincaré inequalities for composition operators with \(L^\varphi -\)norm ⋮ Global Poincaré inequalities for the composition of the sharp maximal operator and Green's operator with Orlicz norms ⋮ 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 ⋮ Weak and strong type estimates for multilinear Calderón-Zygmund operators on differential forms

Cites Work

• Uniform domains and the quasi-hyperbolic metric
• The monotonic property of \(L^s(\mu)\)-averaging domains and weighted weak reverse Hölder inequality
• Hardy-Littlewood theorems for \(A\)-harmonic tensors
• \(L^{s}(\mu)\)-averaging domains
• Orlicz-Hardy inequalities
• Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
• Weighted integral inequalities for solutions of the \(A\)-harmonic equation
• Separable anisotropic differential operators in weighted abstract spaces and applications
• Weighted Poincaré-type estimates for conjugate \(A\)-harmonic tensors
• L^p-averaging domains and the Poincaré inequality
• Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds
• Whitney covers and quasi-isometry of \(L^s(\mu)\)-averaging domains
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