Abstract:

The upper space in Cⁿ is an unbounded domain which cannot be biholomorphically equivalent to any bounded domain, and its boundary is the real hyperplane in Cⁿ. The Cauchy type integral with Bochner-Martinelli kernel in the  upper space in Cⁿ can be defined in some sense. In this paper, by using this Cauchy type integral, the Bochner-Martinelli type singular integral  on the real hyperplane in Cⁿ is studied, and the Cauchy principal value and the Plemelj formula are obtained.

Key words: Real hyperplane, Bochner-Martinelli kernel, Singular integral, Plemelj formula