Integrable Harmonic Functions on Symmetric Spaces of Rank One

Yaakov Ben Natan, Yitzhak Weit

Research output: Contribution to journalArticlepeer-review


If f ∈L1(dμ) is harmonic in the spaceG/K, whereμis a radial measure withμ(G/K)=1, we have, by the mean value propertyf=f*μ. Conversely, does this mean value property imply thatfis 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 measuresμion a symmetric space of rank one for whichf*μi=fimply thatfis harmonic.

Original languageEnglish
Pages (from-to)141-149
Number of pages9
JournalJournal of Functional Analysis
Issue number1
StatePublished - 1 Dec 1998

Bibliographical note

Funding Information:
* Sponsored by the Edmund Landau Center for research in Mathematical supported by the Minerva Foundation (Germany).


  • Harmonic functions; mean value property; symmetric spaces of rank one

ASJC Scopus subject areas

  • Analysis


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