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Generalized Integration Operators from Mixed-Norm to Zygmund-Type Spaces

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Abstract

Let \(\varphi \) be an analytic self-map of the unit disk \(\mathbb {D},\,H(\mathbb {D})\) the space of analytic functions on \({\mathbb {D}}\), and \(g \in H(\mathbb {D}).\) The boundedness and compactness of the generalized integration operator

$$\begin{aligned} I^{(n)}_{g,\varphi }f(z)=\int \limits ^{z}_{0}f^{(n)}(\varphi (\xi ))g(\xi )\mathrm{d}\xi , \quad z\in \mathbb {D}, \end{aligned}$$

from mixed-norm space to the Zygmund-type space, and the little Zygmund-type space are investigated in this article.

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Acknowledgments

The authors acknowledge gratefully the support in part by the Natural Science Foundation of China (11171285) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors also thank the referees for their thoughtful comments and helpful suggestions.

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Authors and Affiliations

  1. Jiangsu Building Vocational and Technical College, Xuzhou, 221116, China

    Jian Guo

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Yongmin Liu

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  1. Jian Guo
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  2. Yongmin Liu
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Correspondence to Yongmin Liu.

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Communicated by Poom Kumam.

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Guo, J., Liu, Y. Generalized Integration Operators from Mixed-Norm to Zygmund-Type Spaces. Bull. Malays. Math. Sci. Soc. 39, 1043–1057 (2016). https://doi.org/10.1007/s40840-015-0204-3

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  • DOI: https://doi.org/10.1007/s40840-015-0204-3

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