Young's convolution inequality on locally compact groups

Young's convolution inequality is one of the elementary inequalities in functional and harmonic analysis, and this inequality is related to various theories in mathematics, physics, and computer theory. In addition, it is known that Young's inequality can be generalized to any locally compact group. In this talk, we introduce the definition of locally compact groups and the statement of Young's inequality with several examples. Finally, we see the speaker's recent results about refining Young's inequality for several locally compact groups, including the special linear groups.