, Volume 17, Issue 3, pp 899-910

On a vector-valued Hopf–Dunford–Schwartz lemma

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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 Fefferman–Stein inequalities in the setting of Dunkl analysis where covering methods are not available.