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<p>We establish a necessary and sufficient condition on weight functions for the boundedness of the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces. In particular, we get similar results for the dual operator of the discrete Hardy operator. We give sufficient pointwise conditions on generalized Φ-functions that guarantee continuous embeddings between weighted Musielak-Orlicz sequence spaces. The results are illustrated by a number of corollaries.</p>

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A boundedness criterion for the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Rovshan Bandaliyev,
  • Mehraly Aliyev,
  • Konul Omarova

摘要

We establish a necessary and sufficient condition on weight functions for the boundedness of the discrete Hardy operator on weighted Musielak-Orlicz sequence spaces. In particular, we get similar results for the dual operator of the discrete Hardy operator. We give sufficient pointwise conditions on generalized Φ-functions that guarantee continuous embeddings between weighted Musielak-Orlicz sequence spaces. The results are illustrated by a number of corollaries.