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In this chapter, we prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces).

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Morrey-Type and Herz Spaces

  • 章节

  • 发表日期：

    2026年

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  • Vakhtang Kokilashvili,
  • Alexander Meskhi,
  • Humberto Rafeiro,
  • Stefan Samko

摘要

In this chapter, we prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces).