On the Behavior of Harmonic Functions Near a Boundary Point

DOI10.2307/2001049zbMath0646.31006OpenAlexW4249521666MaRDI QIDQ3789866

David C. Ullrich, Wade C. Ramey

Publication date: 1988

Full work available at URL: https://doi.org/10.2307/2001049

zbMATH Keywords

boundary pointnormal familiesnon-tangential limitsPoisson integralspositive harmonic functionsweak*-compactnesssectorial limits

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items

Pointwise Fatou theorem for generalized harmonic functions -- normal boundary values ⋮ On parabolic convergence of positive solutions of the heat equation ⋮ Boundary behavior of positive solutions of the heat equation on a stratified Lie group ⋮ Fatou theorem and its converse for positive eigenfunctions of the Laplace-Beltrami operator on harmonic \textit{NA} groups ⋮ On the boundary behavior of positive solutions of elliptic differential equations ⋮ Subordination of regular kernels and abelian theorems for quotients ⋮ On the pointwise converse of Fatou's theorem for Euclidean and real hyperbolic spaces ⋮ Problème de Fatou ponctuel et dérivabilité des mesures. (Pointwise Fatou problem and differentiability of measures)

Cites Work

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• The pointwise Fatou theorem and its converse for positive pluriharmonic functions
• \(H^p\) spaces of several variables
• The Fatou theorem and its converse
• Harmonic Functions and Tauberian Theorems
• Extensions of Hardy spaces and their use in analysis
• Boundary values of bounded holomorphic functions of several variables
• The Converse of the Fatou Theorem for Positive Harmonic Functions

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