On the Converse of Prékopa's Theorem and Berndtsson's Theorem

Wang Xu, Hui Yang

Given a continuous function $\varphi$ defined on a domain $\Omega \subset {\mathbb{R}}^m\times {\mathbb{R}}^n$, we show that if a Prékopa-type result holds for $\varphi +\psi$ for any non-negative convex func…