The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees

DOI10.1090/S0002-9947-07-04433-9zbMath1190.05043OpenAlexW2015550678MaRDI QIDQ3506720

Laura Atanasi, Massimo A. Picardello

Publication date: 17 June 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-07-04433-9

zbMATH Keywords

treesadmissible convergenceLusin area integralboundary behavior of harmonic functionslocal fatou theorem

Mathematics Subject Classification ID

Trees (05C05) Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions (31A20)

Related Items (4)

Universal properties of harmonic functions on trees ⋮ An area theorem for joint harmonic functions on the product of homogeneous trees ⋮ Moments of Riesz measures on Poincaré disk and homogeneous tree -- A comparative study ⋮ Frequently dense harmonic functions and universal martingales on trees

Cites Work

• Admissible convergence of Poisson integrals in symmetric spaces
• On the theory of harmonic functions of several variables. II: Behaviour near the boundary
• The Green formula and \(H^ p\) spaces on trees
• Asymptotic behaviour of harmonic functions in negative curvature
• Local Fatou Theorem and Area Theorem for Symmetric Spaces of Rank One
• A Maximal Function Characterization of the Class H p
• On the Behaviour of Harmonic Functions at the Boundary
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