Stein流形上的奇异积分方程

Singular Integral Equations on Stein Manifolds

文中对积分密度加上适当条件后,应用Stein流形M上具B-M核的B-M型积分的Plemelj公式得到具B-M核的奇异积分的合成公式,应用它讨论了定义在一相对紧区域D的边界上的一类常系数线性奇异积分方程的解。

Let M be a Stein manifold, by ussing Plemelj formula of the B-M type integral, under suitable condition of density, the composite formula of singular integral with B-M kernel is obtained, utilizing this formula the solution of a class of linear singular integral equations with constant coefficients which define on the boundary of a relative com-pact domain D on M is discussed.