A subexponential vector-valued Bohnenblust-Hille type inequality

TL;DR

This paper extends the subexponential bounds of the polynomial Bohnenblust-Hille inequality from complex scalars to vector-valued polynomials on complex Banach lattices, improving understanding of these inequalities.

Contribution

It establishes subexponential bounds for vector-valued polynomial Bohnenblust-Hille inequalities on complex Banach lattices, generalizing previous scalar results.

Findings

Subexponential bounds for vector-valued inequalities on Banach lattices

Recovery of best known constants for classical polynomial inequalities

Extension of scalar inequalities to vector-valued settings

Abstract

Bayart, Pellegrino and Seoane recently proved that the polynomial Bohnenblust--Hille inequality for complex scalars is subexponential. We show that a vector valued polynomial Bohnenblust-Hille inequality on complex Banach lattices is also subexponential for some special cases. Our main result result recovers the best known constants of the classical polynomial inequality provided in \cite{bps}.