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<p>This paper systematically investigates the boundedness and compactness properties of composition operators acting between two Campanato type spaces. The obtained results not only generalize several classical findings on analytic Campanato spaces but also provide a significant improvement over existing literature. Notably, a specific case of our main theorem confirms a conjecture proposed by J. Xiao and W. Xu in The Journal of Geometric Analysis, 24 (2014), 649–666. As an important corollary, we prove that all composition operators are bounded on Campanato type spaces containing BMOA. This conclusion extends the well-known theorem regarding bounded composition operators on BMOA to the broader framework of Campanato type spaces.</p>

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Composition Operators Between Campanato Type Spaces

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Ding Nan,
  • Hasi Wulan

摘要

This paper systematically investigates the boundedness and compactness properties of composition operators acting between two Campanato type spaces. The obtained results not only generalize several classical findings on analytic Campanato spaces but also provide a significant improvement over existing literature. Notably, a specific case of our main theorem confirms a conjecture proposed by J. Xiao and W. Xu in The Journal of Geometric Analysis, 24 (2014), 649–666. As an important corollary, we prove that all composition operators are bounded on Campanato type spaces containing BMOA. This conclusion extends the well-known theorem regarding bounded composition operators on BMOA to the broader framework of Campanato type spaces.