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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-5,
author = {Massimo A. Picardello},
title = {Local admissible convergence of harmonic functions on non-homogeneous trees},
journal = {Colloquium Mathematicae},
volume = {120},
year = {2010},
pages = {419-444},
zbl = {1215.05032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-5}
}
Massimo A. Picardello. Local admissible convergence of harmonic functions on non-homogeneous trees. Colloquium Mathematicae, Tome 120 (2010) pp. 419-444. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm118-2-5/