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The Nonlinear Superposition Operators Between Zygmund-Type and Bloch-Type Spaces

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Abstract

Let \(\varphi \) be a complex-valued function in the plane \({\mathbb {C}}.\) The superposition operator is defined by \( S_\varphi (f)=\varphi \circ f\). In this paper, we characterize the nonlinear superposition operators \(S_\varphi \) acting between the Zygmund-type and Bloch-type spaces in terms of the order and type or the degree of \(\varphi \).

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Acknowledgements

The authors warmly thank the anonymous referee for many suggestions which helped to improve the quality of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, People’s Republic of China

    Yu-Xia Liang

  2. School of Mathematics, Tianjin University, Tianjin, 300354, People’s Republic of China

    Ze-Hua Zhou

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  1. Yu-Xia Liang
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  2. Ze-Hua Zhou
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Correspondence to Ze-Hua Zhou.

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This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11771323 and 11701422).

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Liang, YX., Zhou, ZH. The Nonlinear Superposition Operators Between Zygmund-Type and Bloch-Type Spaces. Mediterr. J. Math. 16, 39 (2019). https://doi.org/10.1007/s00009-019-1304-3

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  • DOI: https://doi.org/10.1007/s00009-019-1304-3

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