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Regularity of spherical means and localization of spherical harmonic expansions
Published online by Cambridge University Press: 09 April 2009
Abstract
Let G/K be a compact symmetric space, and let G = KAK be a Cartan decomposition of G. For f in L1(G) we define the spherical means f(g, t) = ∫k∫k ∫(gktk′) dk dk′, g ∈ G, t ∈ A. We prove that if f is in Lp(G), 1 ≤ p ≤ 2, then for almost every g ∈ G the functions t → f(g, t) belong to certain Soblev spaces on A. From these regularity results for the spherical means we deduce, if G/K is a compact rank one symmetric space, a theorem on the almost everywhere localization of spherical harmonic expansions of functions in L2 (G/K).
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 41 , Issue 3 , December 1986 , pp. 287 - 297
- Copyright
- Copyright © Australian Mathematical Society 1986
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