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The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications

Journal of Inequalities and Applications volume 2006, Article number: 90742 (2006) Cite this article

Abstract

Let be the unit polydisc of and a holomorphic self-map of., and denote the-Bloch space, little-Bloch space, and little star-Bloch space in the unit polydisc, respectively, where. This paper gives the estimates of the essential norms of bounded composition operators induced by between ( or) and ( or). As their applications, some necessary and sufficient conditions for the (bounded) composition operators to be compact from ( or) into ( or) are obtained.

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Affiliations

  1. Department of Mathematics, Tianjin University, Tianjin, 300072, China

    Zehua Zhou & Yan Liu

Authors
  1. Zehua Zhou
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  2. Yan Liu
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Correspondence to Zehua Zhou.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhou, Z., Liu, Y. The essential norms of composition operators between generalized Bloch spaces in the polydisc and their applications. J Inequal Appl 2006, 90742 (2006). https://doi.org/10.1155/JIA/2006/90742

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  • DOI: https://doi.org/10.1155/JIA/2006/90742

Keywords

  • Composition Operator
  • Bloch Space
  • Essential Norm
  • Bound Composition Operator
  • Unit Polydisc