Bohnenblust--Hille inequality for polynomials whose monomials have uniformly bounded number of variables

TL;DR

This paper proves that the constants in a Bohnenblust--Hille type inequality for certain polynomials are uniformly bounded regardless of the degree, using a novel approach that differs from previous methods.

Contribution

It introduces a new method to establish uniform bounds for the inequality's constants, improving upon prior polynomial-growth results.

Findings

Constants are uniformly bounded for all degrees m.

New approach differs from previous techniques.

Results apply to polynomials with monomials having a bounded number of variables.

Abstract

In 2015, using an innovative technique, Carando, Defant and Sevilla-Peris succeeded in proving a Bohnenblust--Hille type inequality with constants of polynomial growth in $m$ for a certain family of complex $m$-homogeneous polynomials. In the present paper, using a completely different approach, we prove that the constants of this inequality are uniformly bounded irrespectively of the value of $m$.