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Kahane-Khinchine type inequalities for negative exponent

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Olivier Guédon
Olivier Guédon
Affiliation:
Université de Marne La Vallée, Equipe d'Analyse et de Mathématiques Appliquées, Cité Descartes, 5 Boulevard Descartes, Champs sur Marne, 77454 Marne la Vallée Cedex 2, France.
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Abstract

We prove a concentration inequality for δ-concave measures over ℝn. Using this result, we study the moments of order q of a norm with respect to a δ-concave measure over ℝn. We obtain a lower bound for q∈ ]−1, 0] and an upper bound for q∈ ]0,+ ∞[ in terms of the measure of the unit ball associated to the norm. This allows us to give Kahane-Khinchine type inequalities for negative exponent.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 165 - 173
Copyright
Copyright © University College London 1999

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