Pitt’s inequality and the uncertainty principle

Beckner, William

doi:10.1090/S0002-9939-1995-1254832-9

Pitt’s inequality and the uncertainty principle
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by William Beckner

Proc. Amer. Math. Soc. 123 (1995), 1897-1905

DOI: https://doi.org/10.1090/S0002-9939-1995-1254832-9

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Abstract:

The "uncertainty principle" is formulated using logarithmic estimates obtained from a sharp form of Pitt’s inequality. The qualitative nature of this result underlies the relations connecting entropy, the Hardy-Littlewood-Sobolev inequality, and the logarithmic Sobolev inequality.

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