On a vector-valued Hopf-Dunford-Schwartz lemma

TL;DR

This paper proposes a conjecture for a vector-valued Hopf-Dunford-Schwartz lemma, provides partial results, and applies it to establish Fefferman-Stein inequalities within Dunkl analysis, where traditional methods fail.

Contribution

It introduces a conjecture for a vector-valued Hopf-Dunford-Schwartz lemma and applies it to Dunkl analysis, extending classical inequalities to new settings.

Findings

Partial proof of the vector-valued Hopf-Dunford-Schwartz lemma

Fefferman-Stein inequalities established in Dunkl analysis

Demonstrates applicability where classical tools are ineffective

Abstract

In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis where the classical tools of real analysis cannot be applied.