Random vectors satisfying Khinchine–Kahane type inequalities for linear and quadratic forms

We study the behaviour of moments of order p (1 < p < ∞) of affine and quadratic forms with respect to non log‐concave measures and we obtain an extension of Khinchine–Kahane inequality for new families of random vectors by using Pisier's inequalities for martingales. As a consequence, we get some estimates for the moments of affine and quadratic forms with respect to a tail volume of the unit ball of lⁿ_q (0 < q < 1). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)