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<p>In this paper, we present a simplified proof of the boundedness of the Hardy operator and its dual on Herz spaces. Our argument relies on an equivalent characterization of Herz spaces in terms of weighted Lebesgue spaces, together with the boundedness of the Hardy operator on these weighted spaces. Our results can be viewed as a new variation of the previous works concerning the application of equivalent norms of Herz spaces in terms of weighted Lebesgue spaces.</p>

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A Short Proof of the Boundedness of the Hardy Operator on Homogeneous Herz Spaces

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Denny Ivanal Hakim,
  • Daniel Salim,
  • Yoshihiro Sawano,
  • Paul Taniwan

摘要

In this paper, we present a simplified proof of the boundedness of the Hardy operator and its dual on Herz spaces. Our argument relies on an equivalent characterization of Herz spaces in terms of weighted Lebesgue spaces, together with the boundedness of the Hardy operator on these weighted spaces. Our results can be viewed as a new variation of the previous works concerning the application of equivalent norms of Herz spaces in terms of weighted Lebesgue spaces.