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Superposition operators between normal weight bloch spaces

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Abstract

Let \(\varphi \) be an entire function, the superposition operator is defined by \(S_{\varphi }(f)=\varphi \circ f\). In this paper, we characterize the entire functions \(\varphi \) that transform weighted Bloch spaces of analytic functions \({\mathcal {B}}_{\mu }\) into another space of the same kind \({\mathcal {B}}_{\nu }\) by superposition. Both \(\mu \) and \(\nu \) are normal functions or both belong to a certain class of functions. We also obtain several results about the boundedness of superposition operators acting between Logarithmic-type Bloch spaces, weight Banach spaces among others.

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Acknowledgements

The authors would like to thank the referees of this paper for their careful reading and useful suggestions.

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  1. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, Hunan, China

    Pengcheng Tang

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  1. Pengcheng Tang
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Correspondence to Pengcheng Tang.

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Communicated by Adrian Constantin.

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The research is supported by the National Natural Science Foundation of China (No. 11942109).

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Tang, P. Superposition operators between normal weight bloch spaces. Monatsh Math 202, 637–653 (2023). https://doi.org/10.1007/s00605-023-01887-2

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