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Hardy Type Spaces and Bergman Type Classes of Complex-Valued Harmonic Functions

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Abstract

The main purpose of this paper is to discuss Hardy type spaces and Bergman type classes of complex-valued harmonic functions. We first establish a Hardy-Littlewood type theorem on complex-valued harmonic functions. Next, the relationships between the Bergman type classes and the Hardy type spaces of complex-valued harmonic functions or the relationships between the Bergman type classes and the Hardy type spaces of harmonic \((K,K')\)-elliptic mappings will be discussed, where \(K\ge 1\) and \(K'\ge 0\) are constants.

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Acknowledgements

The authors would like to thank the referee for many valuable suggestions. The research of the first author was partly supported by the National Science Foundation of China (Grant No. 12071116), the Hunan Provincial Natural Science Foundation of China (No. 2022JJ10001), 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 No. JP22K03363.

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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, Hunan, 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

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  1. Shaolin Chen
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  2. Hidetaka Hamada
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Correspondence to Shaolin Chen.

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Communicated by Rosihan M. Ali.

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Chen, S., Hamada, H. Hardy Type Spaces and Bergman Type Classes of Complex-Valued Harmonic Functions. Bull. Malays. Math. Sci. Soc. 46, 138 (2023). https://doi.org/10.1007/s40840-023-01540-z

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