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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.

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Acknowledgments

We would like to thank the referee for carefully reading this paper and providing valuable improvements and references.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, UMR 8524, Université Lille 1, Cité Scientifique, 59650 , Villeneuve d’Ascq, France

    S. Charpentier

  2. Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4, Place Jussieu, 75005 , Paris, France

    L. Deleaval

Authors
  1. S. Charpentier
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  2. L. Deleaval
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Correspondence to S. Charpentier.

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Charpentier, S., Deleaval, L. On a vector-valued Hopf–Dunford–Schwartz lemma. Positivity 17, 899–910 (2013). https://doi.org/10.1007/s11117-012-0211-7

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  • DOI: https://doi.org/10.1007/s11117-012-0211-7

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