Variants of Miyachi's theorem for Nilpotent Lie groups

Ali Baklouti, Sundaram Thangavelu


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.



Uncertainty principles, Plancherel formula, nilpotent Lie groups

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Journal of the Austral. Maths Soc, copyright Australian Mathematical Society.