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Difference of Composition Operators on Some Analytic Function Spaces

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Abstract

For two analytic self-maps φ and ψ defined on the unit disk ⅅ, we characterize completely the boundedness and compactness of the difference Cφ − Cψ of the composition operators Cφ and Cψ from Bloch space B into Besov space \(B_\nu ^\infty \). Moreover, we also give a complete characterization of the compactness of the difference Cφ − Cψ on BMOA space.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading of the paper and helpful suggestions. The authors also would like to thank Dr. Lijia Ding for his useful suggestion for this paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, P. R. China

    Jun Mei Fan, Yu Feng Lu & Yi Xin Yang

Authors
  1. Jun Mei Fan
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  2. Yu Feng Lu
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  3. Yi Xin Yang
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Correspondence to Yi Xin Yang.

Additional information

Supported by the National Natural Science Foundation of People’s Republic of China (Grant Nos. 12031002 and 11971086)

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Fan, J.M., Lu, Y.F. & Yang, Y.X. Difference of Composition Operators on Some Analytic Function Spaces. Acta. Math. Sin.-English Ser. 37, 1384–1400 (2021). https://doi.org/10.1007/s10114-021-0480-9

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