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).
- AMS subject classification: 31B10, 32M15
ASJC Scopus subject areas
- Algebra and Number Theory