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The Cauchy–Szegö kernel for the Hardy space of 0-regular functions on the quaternionic Siegel upper half space

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Abstract

The notation of 0-regular functions is one of quaternionic counterparts of the notation of holomorphic functions of several complex variables. In this paper, we study the Hardy space of 0-regular functions on the quaternionic Siegel upper half space, which can be identified with a Hilbert subspace of the space of \(L^2\)-integrable functions defined on the boundary. We characterize the kernel of the orthogonal projection to this subspace, the Cauchy–Szegö kernel, and give the explicit formula of this kernel.

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  1. Department of Mathematical Science, Zhejiang Sci-Tech University, Zhejiang, 310018, People’s Republic of China

    Tiren Huang & Ruiwen Wang

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  1. Tiren Huang
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  2. Ruiwen Wang
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Correspondence to Ruiwen Wang.

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Huang, T., Wang, R. The Cauchy–Szegö kernel for the Hardy space of 0-regular functions on the quaternionic Siegel upper half space. Anal.Math.Phys. 12, 141 (2022). https://doi.org/10.1007/s13324-022-00720-7

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