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
The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sh...The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.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.
文摘The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.
