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Composition operators on Bloch and Hardy type spaces

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Abstract

The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic functions in Bloch type spaces with respect to the pseudo-hyperbolic metric, which gives an answer to an open problem. Then some classes of composition operators on Bloch and Hardy type spaces will be investigated. The obtained results improve and extend some corresponding known results.

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Acknowledgements

The research of the first author was partly supported by the National Science Foundation of China (grant no. 12071116), the Hunan Natural Science outstanding youth fund project, the Key Projects of Hunan Provincial Department of Education (grant no. 21A0429); the Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469), the Science and Technology Plan Project of Hunan Province (2016TP1020), and the Discipline Special Research Projects of Hengyang Normal University (XKZX21002); The research of the second author was partly supported by JSPS KAKENHI Grant Number JP19K03553; The research of the third author was partly supported by the National Science Foundation of China (grant nos. 11501220 and 11971182), and Fujian Natural Science Foundation (grant nos. 2021J01304 and 2019J01066).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hengyang Normal University, Hengyang, 421002, Hunan, People’s Republic of China

    Shaolin Chen

  2. Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Changsha, 421002, People’s Republic of China

    Shaolin Chen

  3. Faculty of Science and Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka, 813-8503, Japan

    Hidetaka Hamada

  4. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China

    Jian-Feng Zhu

Authors
  1. Shaolin Chen
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  2. Hidetaka Hamada
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  3. Jian-Feng Zhu
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Correspondence to Shaolin Chen.

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Chen, S., Hamada, H. & Zhu, JF. Composition operators on Bloch and Hardy type spaces. Math. Z. 301, 3939–3957 (2022). https://doi.org/10.1007/s00209-022-03046-z

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