A generalized Kahane-Khinchin inequality

Kahane-Khinchin type Averages

We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on Rn. This is an application of small ball estimate and Chernoff’s method, that has been recently used in the context of Asymptotic Geometric Analysis in [1], [2].

The Khinchin–kahane Inequality and Banach Space Embeddings for Metric Groups

We extend the Khinchin–Kahane inequality to an arbitrary abelian metric group G . In the special case where G is normed, we prove a refinement which is sharp and which extends the sharp version for Banach spaces. We also provide an alternate proof for normed metric groups as a consequence of a general “transfer principle”. This transfer principle has immediate applications to stochastic inequal...

An Extension of the Kahane-khinchine Inequality

(2) r n N I I P Ï 1/p r n N \\} E j ; ^ J >cp ExyTM>*J fr )l lli==1 II ; l l l i = 1 II ) Recalling that in general {E| f ^ } 1 ^ decreases to exp E log \f\ as p decreases to zero, one sees that (1) is a strictly stronger statement than (2); in fact (1) says simply that cp may be taken bounded away from zero in (2). Note that the inequality obtained from (1) by replacing ej with the jth Rademac...

Kahane-Khinchin’s inequality for quasi-norms

We extend the recent results of R. Lata la and O. Guédon about equivalence of Lq-norms of logconcave random variables (KahaneKhinchin’s inequality) to the quasi-convex case. We construct examples of quasi-convex bodies Kn ⊂ IRn which demonstrate that this equivalence fails for uniformly distributed vector on Kn (recall that the uniformly distributed vector on a convex body is logconcave). Our e...

A generalization of Cauchy-Khinchin-van Dam inequality