## Abstract

We find some L^{q}-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 L^{q}-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 language | English |
---|---|

Pages (from-to) | 123-144 |

Number of pages | 22 |

Journal | Integral Equations and Operator Theory |

Volume | 23 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1995 |

## Keywords

- AMS subject classification: 31B10, 32M15

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

## Fingerprint

Dive into the research topics of 'L^{q}-Estimates of spherical functions and an invariant mean-value property'. Together they form a unique fingerprint.