Coefficients of Multilinear Forms on Sequence Spaces

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. 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 (Linear Algebra Appl 331:1–9, 2001), Albuquerque et al. (J Funct Anal 266:3726–3740, 2016), Aron et al. (Linear Algebra Appl 531:399–422, 2017), Albuquerque and Rezende (Commun Contemp Math 20:1750087, 2018), Paulino (Rend Circ Mat Palermo 69:369–380, 2020), among others.