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Essential norms of composition operators between Bloch type spaces in the polydisk

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Abstract

In 2010, Ruhan Zhao obtained the essential norms of composition operators between Bloch type spaces in the disk by the nth power of the induced analytic function. This paper will generalize Zhao’s results to the polydisk. Unlike the case of the composition operators on the unit disk, the essential norms are different for the cases \({p \in (0,1)}\) and p ≥ 1.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China

    Zhong-Shan Fang

  2. Department of Mathematics, Tianjin University, Tianjin, 300072, People’s Republic of China

    Zhong-Shan Fang & Ze-Hua Zhou

Authors
  1. Zhong-Shan Fang
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  2. Ze-Hua Zhou
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Corresponding author

Correspondence to Ze-Hua Zhou.

Additional information

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 10971153, 10671141).

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Fang, ZS., Zhou, ZH. Essential norms of composition operators between Bloch type spaces in the polydisk. Arch. Math. 99, 547–556 (2012). https://doi.org/10.1007/s00013-012-0457-0

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  • DOI: https://doi.org/10.1007/s00013-012-0457-0

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