Integrability of Superharmonic Functions and Subharmonic Functions

DOI10.2307/2160174zbMath0792.31002OpenAlexW4242307502MaRDI QIDQ4281744

Hiroaki Aikawa

Publication date: 31 July 1994

Full work available at URL: https://doi.org/10.2307/2160174

zbMATH Keywords

Green functionsubharmonic functionsubharmonic functionssuperharmonic functioncoarea formula

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05)

Related Items (11)

Superharmonic functions in Hölder domains ⋮ Stability of the mean value formula for harmonic functions in Lebesgue spaces ⋮ Estimates for Dirichlet heat kernels, intrinsic ultracontractivity and expected exit time on Lipschitz domains ⋮ Global integrability of supertemperatures ⋮ Immortal particle for a catalytic branching process ⋮ Densities with the Mean Value Property for Sub-Laplacians: An Inverse Problem ⋮ Densities with the mean value property for harmonic functions in a Lipschitz domain ⋮ Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. I ⋮ A sharp stability result for the Gauss mean value formula ⋮ Default functions and Liouville type theorems based on symmetric diffusions ⋮ Potential theoretic notions related to integrability of superharmonic functions and supertemperatures

Cites Work

• A distortion theorem for conformal mappings with an application to subharmonic functions
• Boundary density and the Green function
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Hausdorff dimension of harmonic measures in the plane
• Superharmonic functions in Hölder domains
• Nonintegrability of Superharmonic Functions
• On Strong Barriers and an Inequality of Hardy for Domains in R ⁿ
• The Integrability of Superharmonic Functions on Lipschitz Domains
• Integrability of Superharmonic Functions on Plane Domains
• Integrability of Superharmonic Functions on Holder Domains of the Plane
• Note on the Integrability of Superharmonic Functions
• Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations.
• On the Global Integrability of Superharmonic Functions in Balls
• Further Results on the Global Integrability of Superharmonic Functions
• Research Problems in Complex Analysis
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