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Integrable Harmonic Functions on Symmetric Spaces of Rank One

✍ Scribed by Yaakov Ben Natan; Yitzhak Weit

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 221 KB
Volume: 160
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3337

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✦ Synopsis

If f # L 1 (d+) is harmonic in the space GÂK, where + is a radial measure with +(GÂK)=1, we have, by the mean value property f = f V +. Conversely, does this mean value property imply that f is harmonic ? In this paper we give a new and natural proof of a result obtained by P. Ahern, A. Flores, W. Rudin (J. Funct. Anal. 11 (1993), 380 397) and A. Koranyi (Contemp. Math. 191 (1995), 107 116) and generalize their result by providing sufficient conditions for a finite set of radial measures + i on a symmetric space of rank one for which f V + i = f imply that f is harmonic.

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