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<p>The main purpose of this paper is to develop some methods to investigate Hardy spaces and composition operators of holomorphic and pluriharmonic functions in bounded symmetric domains. Initially, we prove the completeness of the pluriharmonic Hardy space and establish a Littlewood–Paley type theorem of holomorphic functions in bounded symmetric domains. Next, by using weight, we provide a close relationship between the integral means of pluriharmonic (holomorphic) functions and those of their derivatives in bounded symmetric domains. Additionally, using the weights and the Littlewood–Paley type theorem, the composition operators from the planar harmonic Bloch type spaces to pluriharmonic Hardy spaces in bounded symmetric domains will be discussed. The obtained results provide the improvements and extensions of the corresponding known results.</p>

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Characterizations of Hardy spaces and composition operators in bounded symmetric domains

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Shaolin Chen,
  • Hidetaka Hamada

摘要

The main purpose of this paper is to develop some methods to investigate Hardy spaces and composition operators of holomorphic and pluriharmonic functions in bounded symmetric domains. Initially, we prove the completeness of the pluriharmonic Hardy space and establish a Littlewood–Paley type theorem of holomorphic functions in bounded symmetric domains. Next, by using weight, we provide a close relationship between the integral means of pluriharmonic (holomorphic) functions and those of their derivatives in bounded symmetric domains. Additionally, using the weights and the Littlewood–Paley type theorem, the composition operators from the planar harmonic Bloch type spaces to pluriharmonic Hardy spaces in bounded symmetric domains will be discussed. The obtained results provide the improvements and extensions of the corresponding known results.