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

Jonathan Arazy; Genkai Zhang

doi:10.1007/BF01197533

L^q-Estimates of spherical functions and an invariant mean-value property

Jonathan Arazy
, Genkai Zhang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1007/BF01197533
State	Published - Jun 1995

Keywords

AMS subject classification: 31B10, 32M15

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

Access to Document

10.1007/BF01197533

Cite this

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title = "Lq-Estimates of spherical functions and an invariant mean-value property",

abstract = "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).",

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AB - 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).

KW - AMS subject classification: 31B10, 32M15

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