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Pitt’s inequality for exponential solvable Lie groups with non-trivial center, connected nilpotent Lie groups with non-compact center, Heisenberg motion group and diamond Lie groups has been proved. These inequalities have been used to establish logarithmic uncertainty inequality and Heisenberg uncertainty inequality for the above classes of groups.
Annals of Functional Analysis – Springer Journals
Published: Jul 1, 2023
Keywords: Pitt’s inequality; Logarithmic uncertainty inequality; Fourier transform; Heisenberg uncertainty inequality; Heisenberg motion group; Nilpotent Lie groups; Exponential solvable groups; Plancherel formula; Diamond Lie groups; 43A32; 43A30; 22D10; 22D30; 22E25
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