PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS

摘要

Let D be a bounded domain with piecewise C~((1)) smooth orientable boundary on Stein manifolds, and let Φ(z) be a Cauchy type integral with Bochner-Martinelli kernel Ω(φ~ν, S, S) and Hoelder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t ∈ partial derivD, prove that there exist the interior and outer limit values Φ~±(t) under the meaning of the Cauchy principal value, and obtain the more general Plemelj formula and jump formula.