L q -Estimates of spherical functions and an invariant mean-value property |
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| Authors: | Jonathan Arazy Genkai Zhang |
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| Affiliation: | (1) Department of Mathematics, University of Haifa, 31905 Haifa, Israel;(2) Institut for Matematik og Datalogi, Odense Universitet, DK-5230 Odense M, Denmark;(3) Present address: School of Mathematics, University of New South Wales, 2033 Kensington, N. S. W., Australia |
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| 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). |
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| Keywords: | 31B10 32M15 |
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