A note on multiple summing operators and applications

TL;DR

This paper introduces new theoretical results on multiple summing operators and extends Littlewood's 4/3 inequality to m-linear forms, advancing the understanding of multilinear operator theory.

Contribution

It provides a novel extension of Littlewood's inequality to m-linear forms and new insights into multiple summing operators.

Findings

Extended Littlewood's inequality to m-linear forms.

New results on multiple summing operators.

Enhanced theoretical framework for multilinear analysis.

Abstract

We prove a new result on multiple summing operators and among other applications, we provide a new extension of Littlewood's $4/3$ inequality to $m$-linear forms.