3 papers
math.CA2026
Borell--Brascamp--Lieb inequality with finitely many output functions
Takashi Satomi
The classical Borell--Brascamp--Lieb inequality for multiple functions is an integral inequality relating finitely many input functions to a single output function. In this paper,…
math.CA2026
Continuous solutions of the complex Kac--Bernstein functional equation on the integers and the real numbers
Takashi Satomi
In this paper, the continuous solutions of the complex Kac--Bernstein functional equation \[ f_1 ( u + v ) f_2 ( u - v ) f_1 ( u' + v' ) f_2 ( u' - v' ) = f_1 ( u + v' ) f_2 ( u -…
math.FA2023
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 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 ,…