Kahane-Khinchine type inequalities for negative exponent

Kahane-Khinchine type inequalities for negative exponent

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 t...

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Veröffentlicht in:Mathematika 1999-06, Vol.46 (1), p.165-173
1. Verfasser: Guedon, Olivier
Format: Artikel
Sprache:eng
Schlagworte:
52A40
52A40: CONVEX AND DISCRETE GEOMETRY
CONVEX AND DISCRETE GEOMETRY
General Convexity
Inequalities
Mathematical Physics
Mathematics
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Zusammenfassung: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.
ISSN:0025-5793
2041-7942
DOI:10.1112/S002557930000766X