Almost Everywhere Convergence of Inverse Spherical Transforms on Noncompact Symmetric Spaces

LetGbe a connected noncompact semisimple Lie group with finite center and real rank one. Fix a maximal subgroupK. We considerKbi-invariant functionsfonGand their spherical transformf(λ)=∫Gf(g)ϕλ(g)dg,whereϕλdenote the elementary spherical functions onG/Kandλ⩾0. We consider the maximal operatorsS*f(t...

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Bibliographic Details
Published in:Journal of functional analysis 1997-10, Vol.149 (2), p.277-304
Main Authors: Meaney, C., Prestini, E.
Format: Article
Language:English
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Summary:LetGbe a connected noncompact semisimple Lie group with finite center and real rank one. Fix a maximal subgroupK. We considerKbi-invariant functionsfonGand their spherical transformf(λ)=∫Gf(g)ϕλ(g)dg,whereϕλdenote the elementary spherical functions onG/Kandλ⩾0. We consider the maximal operatorsS*f(t)=SupR>1∫R1f(λ)λ(a(t))|c(λ)|−2dλand prove thatS* maps boundedlyKLKs(G)→Ls(G)+L2(G) for 2n/(n+1)
ISSN:0022-1236
1096-0783
DOI:10.1006/jfan.1997.3123