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<p>In this article, we introduce the concept of Calderón product level sets and use it to characterize the complex interpolation spaces of the closed subspaces with the lattice property for any couple of maximal Banach function spaces (Banach lattices). As applications, we obtain several new results on the complex interpolation of closed subspaces of both Morrey spaces and Lorentz spaces. Moreover, for smooth function spaces having no lattice property, we also study their various closed subspaces and obtain their corresponding complex interpolation results by using their real-variable characterizations.</p>

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Complex Interpolation of Closed Subspaces of Maximal Banach Function Spaces: Calderón Product Level Set Characterizations and Their Applications

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Yoshihiro Sawano,
  • Dachun Yang,
  • Wen Yuan,
  • Mingdong Zhang

摘要

In this article, we introduce the concept of Calderón product level sets and use it to characterize the complex interpolation spaces of the closed subspaces with the lattice property for any couple of maximal Banach function spaces (Banach lattices). As applications, we obtain several new results on the complex interpolation of closed subspaces of both Morrey spaces and Lorentz spaces. Moreover, for smooth function spaces having no lattice property, we also study their various closed subspaces and obtain their corresponding complex interpolation results by using their real-variable characterizations.