## Lie Groups and Representation Theory

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

### 2022/05/17

17:00-18:00   Room #on line (Graduate School of Math. Sci. Bldg.)
Takashi Satomi (The University of Tokyo)
Estimate of the optimal constant of convolution inequalities on unimodular
locally compact groups
(Japanese)
[ Abstract ]
Some convolution inequalities (Young's inequality, the reverse Young's inequality, the Hausdorff--Young inequality) known for a long time on $\mathbb{R}$ can be generalized for any unimodular locally compact group.
In this seminar, we estimate the optimal constants (the ratio of both sides such that these inequalities are optimal) of these inequalities from above and below, and discuss that these estimates are the best for $G=\mathbb{R}$.