Kahane-Khinchine type inequalities for negative exponent

Abstract : We prove a concentration inequality for delta-concave measures over R-n. Using this result, we study the moments of order q of a norm with respect to a delta-concave measure over R-n. We obtain a lower bound for q is an element of ]-1, 0] and an upper bound for q is an element of ]0, + infinity[ 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.