An L p -L q analog of miyachi’s theorem for nilpotent lie groups and sh

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• 作者：F. Abdelmoula ; A. Baklouti ; D. Lahyani
• 关键词：uncertainty principle ; Fourier transform ; Plancherel formula
• 刊名：Mathematical Notes
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：94
• 期：1-2
• 页码：3-19
• 全文大小：755KB
• 参考文献：1. A. Baklouti and S. Thangavelu, “Variant ofMiyachi’s theorem for nilpotent Lie Groups,-J. Aust.Math. Soc. 88(1), 1-7 (2010). CrossRef
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• 作者单位：F. Abdelmoula (1)
  A. Baklouti (1)
  D. Lahyani (1)
  
  1. University of Sfax, Sfax, Tunisia
  
• ISSN：1573-8876

文摘

The purpose of this paper is to formulate and prove an L p -L q analog of Miyachi’s theorem for connected nilpotent Lie groups with noncompact center for 2 ?p, q ?+? This allows us to solve the sharpness problem in both Hardy’s and Cowling-Price’s uncertainty principles. When G is of compact center, we show that the aforementioned uncertainty principles fail to hold. Our results extend those of [1], where G is further assumed to be simply connected, p = 2, and q = +? When G is more generally exponential solvable, such a principle also holds provided that the center of G is not trivial. Representation theory and a localized Plancherel formula play an important role in the proofs.