The singular integral equation on a closed piecewise smooth manifold in C-n

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\(\pounds^ * (\overline D )\), here\(\pounds^ * (\overline D )\) denotes the function set which satisfies the Holder condition on ∂D and holomorphically expands to domainD.