Takashi Satomi

activity

20212026

collaborators

5 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 $Y (p_{1}, p_{2}; G)$ 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 ,…

math.GR2022

An inequality for the convolutions on unimodular locally compact groups and the optimal constant of Young's inequality

Takashi Satomi

Let $μ$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$ . The main result of this paper is that…

math.MG2021

An inequality for the compositions of convex functions with convolutions and an alternative proof of the Brunn-Minkowski-Kemperman inequality

Takashi Satomi

Let $m (G)$ be the infimum of the volumes of all open subgroups of a unimodular locally compact group $G$ . Suppose integrable functions $ϕ_{1}, ϕ_{2} : G \to [0, 1]$ satisfy $\| ϕ_…