VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS

Ali Baklouti, Sundaram Thangavelu

Type: Article

Publication Date: 2010-01-19

Citations: 7

DOI: https://doi.org/10.1017/s144678870900038x

Abstract

Abstract We formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

Locations

Journal of the Australian Mathematical Society - View - PDF

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+	The uncertainty principle: A mathematical survey	1997	Gerald B. Folland Alladi Sitaram
+	Estimate of the Lp-Fourier transform norm on nilpotent Lie groups	2003	Amir Baklouti Kais Smaoui Jean Ludwig
+	The Lp –Lq version of Hardy's Theorem on nilpotent Lie groups	2006	Ali Baklouti Nour Ben Salah
+	On theorems of Beurling and Cowling–Price for certain nilpotent Lie groups	2007	Ali Baklouti Nour Ben Salah
+	Revisiting Hardy's theorem for the Heisenberg group	2002	Sundaram Thangavelu
+	On Hardy’s uncertainty principle for connected nilpotent Lie groups	2007	Ali Baklouti Eberhard Kaniuth
+	Hardy's Theorem for simply connected nilpotent Lie groups	2001	Eberhard Kaniuth Ajay Kumar
+	A Survey of Hardy Type Theorems	2005	Sundaram Thangavelu