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Essential norm of the product of differentiation and composition operators between Bloch-type spaces

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Abstract

In this paper, we give a new characterization for the boundedness of the product of differentiation and composition operators \({C_\varphi D^m}\) acting on Bloch-type spaces and obtain an estimate for its essential norm in terms of the sequence \({\{z^n\}^{\infty}_{n=1}}\), from which the sufficient and necessary condition of compactness of the operator \({C_\varphi D^m}\) follows immediately.

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Authors and Affiliations

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

    Yu-Xia Liang & Ze-Hua Zhou

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  1. Yu-Xia Liang
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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. 10971153, 11126164, 11201331).

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Liang, YX., Zhou, ZH. Essential norm of the product of differentiation and composition operators between Bloch-type spaces. Arch. Math. 100, 347–360 (2013). https://doi.org/10.1007/s00013-013-0499-y

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  • DOI: https://doi.org/10.1007/s00013-013-0499-y

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