A Class Of Singular Integral On Characteristic Manifold

In the thesis, firstly, we generalize Holder's conditions on the characteristic manifold Ω of topological product of the n-dimensional cylinder and m-dimensional half-plane, and then Schwarz's integral formula is discussed on it, and we get a plemelj's formula by using of the method of [2] and [4].Then we obtain both the inversion formula of Hilbert and three new operators S_n+m , T_n+m and k_n+m by the limitary value of the generalized Schwarz's integral formula on the characteristic manifold Ω ,furthermore, their properties are investigated. Finally, we discuss the singular integral equations with constant coefficient about operators S_n+m, T_n+m, K_n+m and several theorems will be gained.