Improved Bounds for Hermite-Hadamard Inequalities in Higher Dimensions

Thomas Beck, Barbara Brandolini, Krzysztof Burdzy +5

Let $\Omega \subset {\mathbb{R}}^n$ be a convex domain and let $f:\Omega \to \mathbb{R}$ be a positive, subharmonic function (i.e. $\Delta f\ge 0$). Then $$ \frac{1}{|Ω|} \int_Ω{f dx} \leq \…