Optimal constants of classical inequalities in complex sequence spaces

TL;DR

This paper determines the best possible constants for classical inequalities like the multiple Khinchine and mixed Littlewood inequalities in complex sequence spaces, advancing the understanding of these fundamental mathematical bounds.

Contribution

It provides the exact optimal constants for key classical inequalities in complex sequence spaces, which were previously unknown or only estimated.

Findings

Optimal constants for multiple Khinchine inequality established

Optimal constants for mixed Littlewood inequality determined

Enhances precision in bounds for inequalities in complex analysis

Abstract

In this paper we obtain the optimal constants of some classical inequalities, such as the multiple Khinchine inequality for Steinhaus variables and the mixed Littlewood inequality for complex scalars.