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Kahane-Khinchine type inequalities for negative exponent. (English) Zbl 0965.26011
Summary: We prove a concentration inequality for \(\delta\)-concave measures over \(\mathbb{R}^n\). Using this result, we study the moments of order \(q\) of a norm with respect to a \(\delta\)-concave measure over \(\mathbb{R}^n\). We obtain a lower bound for \(q\in ]-1,0]\) and an upper bound for \(q\in ]0,+\infty[\) in terms of the measure of the unit ball associated to the norm. This allows us to give Kahane-Khinchine type inequalities for a negative exponent.

MSC:
26D15 Inequalities for sums, series and integrals
26A51 Convexity of real functions in one variable, generalizations
28A12 Contents, measures, outer measures, capacities
60E15 Inequalities; stochastic orderings
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