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New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

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Abstract

Let u be a holomorphic function and φ a holomorphic self-map of the open unit disk \(\mathbb{D}\) in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators uC φ from Zygmund type spaces to Bloch type spaces in \(\mathbb{D}\) in terms of u, φ, their derivatives, and φ n, the n-th power of φ. Moreover, we obtain some similar estimates for the essential norms of the operators uC φ , from which sufficient and necessary conditions of compactness of uC φ follows immediately.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tian** University, No. 92 Wei** Road, Nankai District, Tian**, 300072, P.R. China

    **n-Cui Guo & Ze-Hua Zhou

  2. Center for Applied Mathematics, Tian** University, 92 Wei**g Road, Nankai District, Tian**, 300072, P.R. China

    Ze-Hua Zhou

Authors
  1. **n-Cui Guo
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  2. Ze-Hua Zhou
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Correspondence to Ze-Hua Zhou.

Additional information

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11371276, 11301373, 11201331).

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Guo, XC., Zhou, ZH. New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces. Czech Math J 65, 331–346 (2015). https://doi.org/10.1007/s10587-015-0178-1

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  • DOI: https://doi.org/10.1007/s10587-015-0178-1

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