Boundedness of composition operators on Morrey spaces and weak Morrey spaces

Naoya Hatano, Masahiro Ikeda, Isao Ishikawa, Yoshihiro Sawano

Research output: Contribution to journalArticlepeer-review

Abstract

In this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As this specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.

Original languageEnglish
Article number69
JournalJournal of Inequalities and Applications
Volume2021
Issue number1
DOIs
Publication statusPublished - 2021

Keywords

  • Boundedness
  • Composition operators
  • Morrey spaces
  • Weak Morrey spaces

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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