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The Kunze-Stein phenomenon associated with Jacobi transforms


Author: Jianming Liu
Journal: Proc. Amer. Math. Soc. 133 (2005), 1817-1821
MSC (2000): Primary 33C45; Secondary 43A90, 42B25, 22E30
DOI: https://doi.org/10.1090/S0002-9939-05-07754-3
Published electronically: January 14, 2005
MathSciNet review: 2120282
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently A. D. Ionescu (2000) established the endpoint estimate for the Kunze-Stein phenomenon, which states that if $G$ is a noncompact connected semisimple Lie group of real rank one with finite center, then

\begin{displaymath}L^{2,1}(G)\ast L^{2,1}(G)\subseteq L^{2,\infty }(G). \end{displaymath}

In this paper, we will prove the corresponding result for the Jacobi transform. Our method is analytical, in which we do not use the structure of Lie groups.


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Additional Information

Jianming Liu
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: liujm@math.pku.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-05-07754-3
Keywords: Kunze-Stein phenomenon, Jacobi transform, Lorentz space
Received by editor(s): July 19, 2003
Received by editor(s) in revised form: February 24, 2004
Published electronically: January 14, 2005
Additional Notes: This research was supported by the National Natural Science Foundation of China, Projects 10001002 and 10371004
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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