Guédon, Olivier Kahane-Khinchine type inequalities for negative exponent. (English) Zbl 0965.26011 Mathematika 46, No. 1, 165-173 (1999). 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. Cited in 1 ReviewCited in 23 Documents 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 Keywords:concentration inequality; \(\delta\)-concave measure; Kahane-Khinchine type inequalities PDFBibTeX XMLCite \textit{O. Guédon}, Mathematika 46, No. 1, 165--173 (1999; Zbl 0965.26011) Full Text: DOI References: [1] DOI: 10.1007/BF02767353 · Zbl 0654.46019 [2] Milman, Springer Lecture Notes 1200 (1986) [3] Milman, CR. Acad. Sci. Paris 308 pp 91– (1989) [4] DOI: 10.1007/BF01425510 · Zbl 0292.60004 [5] Latala, MSRI, Publications 34 pp 123– (1998) [6] Kahane, Cambridge Studies in Advanced Math (1985) [7] DOI: 10.1007/BF02018814 [8] DOI: 10.1002/rsa.3240040402 · Zbl 0788.60087 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.