On the generalized Bohnenblust–Hille inequality for real scalars

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

“…The so-called classical Kahane-Salem-Zygmund multilinear inequality provides a unimodular multilinear form mapping ℓ n p × • • • × ℓ n p into K (see [12]). This result is nowadays a fundamental tool in modern analysis with a broad range of applications involving, for instance, the Bohr radius, Bohnenblust-Hille's and Hardy-Littlewood's multilinear inequalities (see, e.g., [1,4,7,9,10,13,14,15,16,17,18,19]).…”

“…The original purpose of this inequality is to provide a unimodular form on (ℓ n p ) d with relatively small supremum norm but relatively large majorant function [12]. Nowadays this result is a formidable tool in modern analysis with a broad range of applications (see, e.g., [1,2,4,7,13,14,15,16,18,19]).…”

Optimal constants of classical inequalities in complex sequence spaces

“…Our goal in this section is to prove the analogue of the estimate (10) for the case of Steinhaus variables. We will prove that the optimal constants S m,p and R m,p are ( A p ) m and ( B p ) m , respectively, for all m ∈ N and for all 0 < p < ∞.…”

“…(n) are unknown, except for K = R and σ = id (and all σ when symmetry arguments are possible), in the following particular cases (see also [2,3,10] for other special cases):…”

Some applications of the regularity principle in sequence spaces

“…The investigation of the optimal constants of the Hardy-Littlewood inequalities (see [1,3,4,5,6]) is motivated by their connection with the important Bohnenblust-Hille inequality (see, for instance [9,15,18,21] and the references therein).…”