The Kunze-Stein phenomenon associated with Jacobi transforms
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- by Jianming Liu PDF
- Proc. Amer. Math. Soc. 133 (2005), 1817-1821 Request permission
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 \[ L^{2,1}(G)\ast L^{2,1}(G)\subseteq L^{2,\infty }(G). \] 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.References
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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
- 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
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2120282