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arXiv · 1908.03040

An explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space and applications

Der-Chen Chang·Xuan Thinh Duong·Ji Li·Wei Wang·Qingyan Wu
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Abstract

In this paper we obtain an explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space, and then based on this, we prove that the Cauchy--Szeg\"{o} projection on quaternionic Heisenberg group is a Calder\'on--Zygmund operator via verifying the size and regularity conditions for the kernel. Next, we also obtain a suitable version of pointwise lower bound for the kernel, which further implies the characterisations of the boundedness and compactness of commutator of the Cauchy--Szeg\"{o} operator via the BMO and VMO spaces on quaternionic Heisenberg group, respectively.

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Der-Chen Chang, Xuan Thinh Duong, Ji Li, Wei Wang, Qingyan Wu. 2019-08-08. An explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space and applications. https://arxiv.org/abs/1908.03040

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