On the Bohnenblust–Hille Inequality for Multilinear Forms

Abstract

The general versions of the Bohnenblust-Hille inequality for m-linear forms are valid for exponents q 1 , ..., q m ∈ [1, 2]. In this paper we show that a slightly different characterization is valid for q 1 , ..., q m ∈ (0, ∞).

Optimal constants for a mixed Littlewood type inequality

“…One of the most for reaching generalizations of the Hardy-Littlewood inequality is the following theorem (see also [25]): Theorem 1.1. (See Albuquerque, Araujo, Núñez, Pellegrino and Rueda [1]) Let m ≥ 2 be a positive integer, 1 ≤ k ≤ m and n 1 , .…”

Asymptotic Estimates for Unimodular Multilinear Forms with Small Norms on Sequence Spaces

“…The search for the optimal constants involved in Bohnenblust-Hille and Hardy-Littlewood inequalities was efficiently developed in the recent years and the best known constant have polynomial growth (see [10,15,16,18]). Kahane-Salem-Zygmund's inequality turns out to be a formidable (but not complete) tool to provide the optimal exponents on both inequalities (see [1,4,20]). Therefore, a question arises: "How efficient the Kahane-Salem-Zygmund is on providing optimal Bohnenblust-Hille or Hardy-Littlewood constants?…”

On unimodular multilinear forms with small norms on sequence spaces

“…The above estimate appears is essence in Bayart's paper [2]. Both the multilinear and polynomial versions of the Kahane-Salem-Zygmund inequalities play a fundamental role in modern Analysis (see, for instance, [3,5,9] and the references therein). However, to the best of the authors' knowledge, despite the existence of more involved abstract generalizations of the Kahane-Salem-Zygmund inequality (see [8]), the best estimate (i.e., the smallest possible exponent for n) for the general case (p 1 , ..., p m ∈ [1, ∞]) of sequence spaces is still unknown.…”