#### Vol. 295, No. 1, 2018

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Extremal pairs of Young's inequality for Kac algebras

### Zhengwei Liu and Jinsong Wu

Vol. 295 (2018), No. 1, 103–121
##### Abstract

In this paper, we prove a sum set estimate and the exact sum set theorem for unimodular Kac algebras. Combining the characterization of minimizers of the Donoso–Stark uncertainty principle and the Hirschman–Beckner uncertainty principle, we characterize the extremal pairs of Young’s inequality and extremal operators of the Hausdorff–Young inequality for unimodular Kac algebras.

##### Keywords
Young's inequality, Kac algebras, sum set, uncertainty principles
##### Mathematical Subject Classification 2010
Primary: 46L89, 58B32