Inequality on the optimal constant of Young's convolution inequality for locally compact groups and their closed subgroups

Takashi Satomi

We define the optimal constant $Y(p_1,p_2;G)$ of Young's convolution inequality as \begin{align} Y ( p_1 , p_2 ; G ) := \sup \{ \| ϕ_1 * ( ϕ_2 Δ^{1 / p_1'} ) \|_p \mid ϕ_1 ,…