Brascamp-Lieb-Luttinger inequalities for convex domains of finite inradius (Q1847925)

The main theorems of this paper are: a multiple integral inequality for convex domains \(D\subseteq \mathbb{R}^n\) of finite inradius \[ R_D:=\sup\{R>0 : \exists \text{ ball of radius } R \text{ in } D\} \] and a sharper inequality in \(\mathbb R^2\). Thus, results from [\textit{R. Banuelos, R. Latala} and \textit{P. J. Méndez-Hernández}, Proc. Am. Math. Soc. 129, 2997-3008 (2001; Zbl 0974.60037)] are generalized. These inequalities yield various new isoperimetric-type inequalities for: Brownian motion, symmetric stable processes (in convex domains of finite inradius) and also to processes whose generators are relativistic Schrödinger operators.