The singular integral equation on a closed piecewise smooth manifold inCn

In this paper, we obtain the general permutation formulas and composition formulas of singular integral of the Bochner-Martinelli type on a closed piecewiseC ⁽¹⁾ smooth manifold. As an application, we consider the corresponding singular integral equation of linear variable coefficients, and prove that the singular integral equation can be transformed to an equivalent Fredholm equation, whose characteristic equation has a unique solution in , here denotes the function set which satisfies the Hölder condition on D and holomorphically expands to domainD.Corresponding author. Project supported in part by the Mathematical Tian Yuan Foundation of China (Grant No. TY10126033).