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

  • Yu-Xia Liang
  • Ze-Hua ZhouEmail author


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 \(\varphi \).


Nonlinearity superposition operator Zygmund-type space Bloch-type space boundedness order 

Mathematics Subject Classification

Primary 47H30 Secondary 30D45 30H05 



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. 1.School of Mathematical SciencesTianjin Normal UniversityTianjinPeople’s Republic of China
  2. 2.School of MathematicsTianjin UniversityTianjinPeople’s Republic of China

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