S. Larson

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math.CA2020

A sharp multidimensional Hermite-Hadamard inequality

Simon Larson

Let $Ω \subset R^{d}$ , $d \geq 2$ , be a bounded convex domain and $f : Ω \to R$ be a non-negative subharmonic function. In this paper we prove the inequality \[ \…

math.CA2019

Improved Bounds for Hermite-Hadamard Inequalities in Higher Dimensions

Thomas Beck, Barbara Brandolini, Krzysztof Burdzy +5

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