An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications
Der‐Chen Chang, Xuan Thinh Duong, Ji Li, Wei Wang, Qingyan Wu
Abstract
In this paper we obtain an explicit formula of Cauchy-Szegö kernel for quaternionic Siegel upper half space, and then based on this, we prove that the Cauchy-Szegö projection on quaternionic Heisenberg group is a Calderón-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-Szegö operator via the BMO and VMO spaces on quaternionic Heisenberg group, respectively.
Topics & Concepts
MathematicsKernel (algebra)Pure mathematicsCauchy distributionSpace (punctuation)Mathematical analysisPhilosophyLinguisticsMathematical Analysis and Transform MethodsAdvanced Algebra and GeometryAlgebraic and Geometric Analysis