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We start by introducing a new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalization of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained.

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Approximation in Subspaces of Morrey Spaces

  • 章节

  • 发表日期：

    2025年

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  • Alexander Meskhi,
  • Humberto Rafeiro,
  • Stefan Samko

摘要

We start by introducing a new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalization of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained.