An explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space and applications
Complex Variables
2019-09-04 v2
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.
Keywords
Cite
@article{arxiv.1908.03040,
title = {An explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space and applications},
author = {Der-Chen Chang and Xuan Thinh Duong and Ji Li and Wei Wang and Qingyan Wu},
journal= {arXiv preprint arXiv:1908.03040},
year = {2019}
}