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

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.

Young's inequality, Kac algebras, sum set, uncertainty principles
Mathematical Subject Classification 2010
Primary: 46L89, 58B32
Received: 14 April 2017
Revised: 16 December 2017
Accepted: 18 December 2017
Published: 13 March 2018
Zhengwei Liu
Department of Mathematics and Department of Physics
Harvard University
Cambridge, MA
United States
Jinsong Wu
Institute for Advanced Study in Mathematics
Harbin Institute of Technology
Harbin, 150001