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The Pluriharmonic Hardy Space and Toeplitz Operators

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Abstract

Compared with harmonic Bergman spaces, this paper introduces a new function space which is called the pluriharmonic Hardy space \(h^{2}(\mathbb {T}^{2})\). We character (semi-) commuting Toeplitz operators on \(h^{2}(\mathbb {T}^{2})\) with bounded pluriharmonic symbols. Interestingly, these results are quite different from the corresponding properties of Toeplitz operators on Hardy spaces, Bergman spaces and harmonic Bergman spaces. Our method for Toeplitz operators on \(h^{2}(\mathbb {T}^{2})\) gives new insight into the study of commuting Toeplitz operators on harmonic Bergman spaces.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Xuanhao Ding & Yuanqi Sang

  2. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Xuanhao Ding

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  1. Xuanhao Ding
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  2. Yuanqi Sang
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Correspondence to Xuanhao Ding.

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Ding, X., Sang, Y. The Pluriharmonic Hardy Space and Toeplitz Operators. Results Math 72, 1473–1497 (2017). https://doi.org/10.1007/s00025-017-0728-y

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  • DOI: https://doi.org/10.1007/s00025-017-0728-y

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