Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 81-90

SOME RESULTS CONCERNING THE p-ROYDEN AND p-HARMONIC BOUNDARIES OF A GRAPH OF BOUNDED DEGREE

Michael J. Puls

CUNY, John Jay College, Department of Mathematics
445 West 59th Street, New York, NY 10019, U.S.A.; mpuls 'at' jjay.cuny.edu

Abstract. Let p be a real number greater than one and let \Gamma be a connected graph of bounded degree. We show that the p-Royden boundary of \Gamma with the p-harmonic boundary removed is an F\sigma-set. We also characterize the p-harmonic boundary of \Gamma in terms of the intersection of the extreme points of a certain subset of one-sided infinite paths in \Gamma.

2010 Mathematics Subject Classification: Primary 60J50; Secondary 43A15, 31C45.

Key words: p-Royden boundary, p-harmonic boundary, p-harmonic function, F\sigma-set, extreme points of a path, p-extremal length of paths.

Reference to this article: M.J. Puls: Some results concerning the p-Royden and p-harmonic boundaries of a graph of bounded degree. Ann. Acad. Sci. Fenn. Math. 37 (2012), 81-90.

Full document as PDF file

doi:10.5186/aasfm.2012.3705

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