Regularity of the coefficients of multilinear forms on sequence spaces

TL;DR

This paper explores regularity techniques for coefficients of multilinear forms on sequence spaces, extending previous theorems and connecting to various mathematical fields.

Contribution

It introduces a regularity technique to optimize parameters, generalizing and extending prior results in the study of multilinear forms.

Findings

Extended theorems of Osikiewicz and Tonge (2001)

Generalized results of Albuquerque et al. (2016)

Connected regularity properties to multiple mathematical fields

Abstract

The investigation of regularity/summability properties of the coefficients of bilinear forms in sequence spaces was initiated by Littlewood in $1930$. Nowadays, this topic has important connections with other fields of Pure and Applied Mathematics as Complex Analysis, Quantum Information Theory, Theoretical Computer Science and Combinatorial Games. In this paper we explore a regularity technique to obtain optimal parameters for several results in this framework, extending/generalizing theorems of Osikiewicz and Tonge ($2001$), Albuquerque \textit{et al.} ($2016$), Aron \textit{et al.} ($2017$), Albuquerque and Rezende ($2018$), Paulino ($2020$), among others.