The singular integral equation on a closed piecewise smooth manifold inC n

In this paper, we obtain the general permutation formulas and composition formulas of singular integral of the BochnerMartinelli type on a closed piecewise C(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 l*(D) , here l*(D) denotes the function set which satisfies the Holder condition on (partial differential)D and holomorphically expands to domain D.