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VOLUME ESTIMATES FOR Lp-ZONOTOPES AND BEST BEST CONSTANTS IN BRASCAMP–LIEB INEQUALITIES
Published online by Cambridge University Press: 10 December 2009
Abstract
Given some unit vectors a1,…,am∈ℝn that span all ℝn and some positive numbers θ1,…,θm, we consider for every p≥1 the convex body We will give some upper bounds for the volume of Kp and some lower bounds for the volume of its polar, depending on some parameters, which improve the ones obtained using the Brascamp–Lieb inequality. We will also see how the best choice of these parameters is related to the transformation which takes Kp to a special position which, for instance, when p=∞, is John’s position.
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- Research Article
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- Copyright © University College London 2010
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