A note on the Bohnenblust--Hille inequality for multilinear forms

TL;DR

This paper revises the Bohnenblust--Hille inequality for multilinear forms, extending the valid exponents from the interval [1,2] to the broader range (0,∞), providing a new characterization.

Contribution

It introduces a new characterization of the Bohnenblust--Hille inequality for exponents in (0,∞), expanding the known valid range beyond [1,2].

Findings

Valid for exponents in (0,∞)

Extends previous results for multilinear forms

Provides a new mathematical characterization

Abstract

The general versions of the Bohnenblust--Hille inequality for $m$-linear forms are valid for exponents $q_{1},...,q_{m}\in \lbrack 1,2].$ In this show that a slightly different characterization is valid for $q_{1},...,q_{m}\in (0,\infty ).$