a1 Department of Mathematics, Faculty of Sciences at Sfax, Route de Soukra, 3038, Sfax, Tunisia (email: [email protected])
a2 Department of Mathematics, Indian Institute of Science, Bangalore 560012, India (email: [email protected])
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.
(Received February 27 2009)
(Accepted August 30 2009)
2000 Mathematics subject classification
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The first author was supported by D.G.R.S.R.T., Research Unity 00 UR 1501 and the second author by a J.C. Bose Fellowship from DST.