The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees
Authors:
Laura Atanasi and Massimo A. Picardello
Journal:
Trans. Amer. Math. Soc. 360 (2008), 3327-3343
MSC (2000):
Primary 05C05; Secondary 31A20
DOI:
https://doi.org/10.1090/S0002-9947-07-04433-9
Published electronically:
November 28, 2007
MathSciNet review:
2379799
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We prove admissible convergence to the boundary of functions that are harmonic on a subset of a homogeneous tree by means of a discrete Green formula and an analogue of the Lusin area function.
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Additional Information
Laura Atanasi
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
Email:
atanasi@mat.uniroma2.it
Massimo A. Picardello
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
Email:
picard@mat.uniroma2.it
DOI:
https://doi.org/10.1090/S0002-9947-07-04433-9
Keywords:
Boundary behavior of harmonic functions,
admissible convergence,
local Fatou theorem,
Lusin area integral,
trees
Received by editor(s):
October 3, 2005
Received by editor(s) in revised form:
October 7, 2006
Published electronically:
November 28, 2007
Article copyright:
© Copyright 2007
Department of Mathematics, University of Rome “Tor Vergata”