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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

David Alonso-Gutiérrez
David Alonso-Gutiérrez*
Affiliation:
Área de Análisis Matemático, Departamento de Matemáticas, Edificio de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain (email: daalonso@unizar.es)
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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.

Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 45 - 60
Copyright
Copyright © University College London 2010

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