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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

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
Published electronically: November 28, 2007
MathSciNet review: 2379799
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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: http://dx.doi.org/10.1090/S0002-9947-07-04433-9
PII: S 0002-9947(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''