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Sharp Shannon's and logarithmic Sobolev inequalities for the Hankel transform
Journal article   Peer reviewed

Sharp Shannon's and logarithmic Sobolev inequalities for the Hankel transform

Saifallah Ghobber
Journal of mathematical analysis and applications, Vol.507(1), p.125740
01/03/2022
DOI: https://doi.org/10.1016/j.jmaa.2021.125740

Abstract

Hankel transform Logarithmic Sobolev inequality Shannon inequality Sobolev inequality Uncertainty principle
The first aim of this paper is to prove Sharp Beckner-type and Shannon-type inequalities for the Hankel transform. Then using Nash's inequality and the generalized Pitt's inequality for the Hankel transform, we prove Sobolev-type and Logarithmic Sobolev-type inequalities. Combining theses results, we derive new uncertainty inequalities in the Hankel setting.

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