Regularity of spherical means and localization of spherical harmonic expansions
1986 ◽
Vol 41
(3)
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pp. 287-297
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Keyword(s):
Rank One
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AbstractLet 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).
2006 ◽
Vol 234
(2)
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pp. 321-363
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Keyword(s):
2018 ◽
Vol 2020
(5)
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pp. 1346-1365
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1992 ◽
Vol 07
(23)
◽
pp. 5781-5796
Keyword(s):
1992 ◽
Vol 03
(05)
◽
pp. 629-651
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1985 ◽
pp. 83-119
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