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<p>We here pose a new problem for composition operators on Bloch and little Bloch spaces. Could a compact composition operator with an analytic symbol imply the compactness of composition operator with product of it and any analytic self-map of the open unit disk? We will investigate the hyperbolic derivative of products of analytic self-maps of the unit disk and so provide explicit and new examples of products that induce compact composition operators on Bloch and little Bloch spaces.</p>

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Composition Operators with Products of Analytic Symbols on Bloch Spaces

  • 期刊论文

  • 发表日期：

    2025年7月24日

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  • Takuya Hosokawa,
  • Shûichi Ohno

摘要

We here pose a new problem for composition operators on Bloch and little Bloch spaces. Could a compact composition operator with an analytic symbol imply the compactness of composition operator with product of it and any analytic self-map of the open unit disk? We will investigate the hyperbolic derivative of products of analytic self-maps of the unit disk and so provide explicit and new examples of products that induce compact composition operators on Bloch and little Bloch spaces.