Integral Equations and Operator Theory

, Volume 23, Issue 2, pp 123–144

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

  • Jonathan Arazy
  • Genkai Zhang
Article

DOI: 10.1007/BF01197533

Cite this article as:
Arazy, J. & Zhang, G. Integr equ oper theory (1995) 23: 123. doi:10.1007/BF01197533

Abstract

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

AMS subject classification

31B1032M15

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  • Jonathan Arazy
    • 1
  • Genkai Zhang
    • 2
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Institut for Matematik og DatalogiOdense UniversitetOdense MDenmark
  3. 3.School of MathematicsUniversity of New South WalesKensingtonAustralia