Local admissible convergence of harmonic functions on non-homogeneous trees

Volume 118 / 2010

Massimo A. Picardello Colloquium Mathematicum 118 (2010), 419-444 MSC: Primary 05C05; Secondary 31A20, 60J45. DOI: 10.4064/cm118-2-5

Abstract

We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.

Authors

  • Massimo A. PicardelloDipartimento di Matematica
    Università di Roma “Tor Vergata”
    Via della Ricerca Scientifica
    00133 Roma, Italy
    e-mail

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