Several maximal inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. The method relies upon Lévy’s inequality and the technique established in [14] which is obtained by Haagerup-Young-Stechkin’s best possible constants in the classical Khintchine inequalities. Moreover by using Donsker’s invariance principle it is shown that the numerical constant in the inequality dedu...

Abstract. We strengthen the usual Csiszár-Kullback-Pinsker inequality by allowing weights in the total variation norm; admissible weights depend on the decay of the reference probability measure. We use this result to derive transportation inequalities involving Wasserstein distances for various exponents: in particular, we recover the equivalence between a T1 inequality and the existence of a ...

In this paper, we generalize Haagerup’s inequality [H] (on convolution norm in the free group) to a very general context of R-diagonal elements in a tracial von Neumann algebra; moreover, we show that in this “holomorphic” setting, the inequality is greatly improved from its originial form. We give an elementary combinatorial proof of a very special case of our main result, and then generalize ...

• Positivity: N(v) ≥ 0 with equality if and only if v = 0. • Positive Homogeneity: N(αv) = |α|N(v). • Triangle Inequality: N(x1 + x2) ≤ N(x1) +N(x2). If N is a norm for V then we call ρ N (x1, x2) := N(x1−x2) the associated distance function (or metric) for V . A vector space V together with some a choice of norm is called a normed space, and the norm is usually denoted by ‖ ‖. If V is complete...

When the space L log+L is given the Hardy-Littlewood norm the best constant in the corresponding version of Zygmund's conjugate function inequality is shown to be r2 3~2 + 5-2 7-2 + • ■ ■ K = I-2 + 3"2 + 5"2 + 7" This complements the recent result of Burgess Davis that the best constant in Kolmogorov's inequality is K"1. The symbol K will be used throughout for the constant p2 _ 3-2 + 5-2 _ 7-2...