TY - JOUR A1 - Frühwirth, Lorenz A1 - Prochno, Joscha T1 - Hölder’s inequality and its reverse — a probabilistic point of view JF - Mathematische Nachrichten N2 - In this article, we take a probabilistic look at Hölder's inequality, considering the ratio of terms in the classical Hölder inequality for random vectors in ℝ𝑛. We prove a central limit theorem for this ratio, which then allows us to reverse the inequality up to a multiplicative constant with high probability. The models of randomness include the uniform distribution on 𝓁𝑛𝑝 balls and spheres. We also provide a Berry–Esseen–type result and prove a large and a moderate deviation principle for the suitably normalized Hölder ratio. KW - Berry–Esseen bound KW - central limit theorem KW - Hölder’s inequality KW - 𝓁 𝑛 𝑝 ball KW - large deviation principle KW - moderate deviation principle KW - reverse inequality Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:101:1-2023062315175042989607 VL - 296 IS - 12 SP - 5493 EP - 5512 PB - Wiley CY - Hoboken ER -