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VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS
Published online by Cambridge University Press: 19 January 2010
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.
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2010
Footnotes
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.
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