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In this paper we obtain an explicit formula of the Cauchy-Szego kernel for quaternionic Siegel upper half space, and then based on this, we prove that the Cauchy-Szego projection on quaternionic Heisenberg group is a Calderon-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-Szego operator via the BMO and VMO spaces on quaternionic Heisenberg group, respectively.
- Cauchy-Szegő kernel
- quaternionic Siegel upper half space
- Calderon- Zygmund kernel
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Li, J., Guo, Z., Kenig, C. & Nakanishi, K.
31/01/17 → …
Duong, X., Hofmann, S., Ouhabaz, E. M. & Wick, B.
11/02/19 → 10/02/22