An extension of the Kahane-Khinchine inequality

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...

An Operator Extension of Bohr's inequality

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...

an operator extension of bohr's inequality

An extension of Maclaurins inequality

Let G be a graph of order n and clique number !: For every x = (x1; : : : ; xn) 2 Rn and 1 s !; set fs (G;x) = X fxi1 : : : xis : fi1; : : : ; isg is an s-clique of Gg ; and let s (G;x) = fs (G;x) ! s 1 : We show that if x 0; then 1 (G;x) 1=2 2 (G;x) 1=! ! (G;x) : This extends the inequality of Maclaurin (G = Kn) and generalizes the inequality of Motzkin and Straus. In addition, if x > 0; for e...