Lq-Estimates of spherical functions and an invariant mean-value property

Jonathan Arazy, Genkai Zhang

Research output: Contribution to journalArticlepeer-review


We find some Lq-estimates for the spherical functions on Cartan domains. As an application we prove that if the rank of the Cartan domain D is greater than one, then for any 1<-q<∞, the invariant mean-value property for Lq-function on D does not imply harmonicity (the converse is known to be true even in the context of general non-compact Riemannian symmetric spaces G/K).

Original languageEnglish
Pages (from-to)123-144
Number of pages22
JournalIntegral Equations and Operator Theory
Issue number2
StatePublished - Jun 1995


  • AMS subject classification: 31B10, 32M15

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory


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