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^V, S^-, S) and Holder continuous density...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^V, S^-, S) and Holder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t∈δD, 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.展开更多
文摘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^V, S^-, S) and Holder continuous density function φ(ζ), the authors define a solid angular coefficient α(t) at the point t∈δD, 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.