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

Atanasi, Laura; Picardello, Massimo

doi:10.1090/S0002-9947-07-04433-9

The Lusin area function and local admissible convergence of harmonic functions on homogeneous trees
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by Laura Atanasi and Massimo A. Picardello PDF

Trans. Amer. Math. Soc. 360 (2008), 3327-3343

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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