复流形上具有非光滑边界的强拟凸域上带权因子的Koppelman-Leray公式

The Koppelman-Leray Formula with Weight Factors for a Strictly Pseudoconvex Domain with Non-Smooth Boundaries on a Complex Manifold

利用权因子，我们得到了复流形上边界不必光滑的强拟凸域上（ｐ，ｑ）微分形式的带权因子的Ｋｏｐｐｅｌｍａｎ－Ｌｅｒａｙ公式及其 －方程的带权因子的解，其特点是不含有边界积分．从而避免了边界积分的复杂估计．其次，引进了权因子，带权因子的积分公式在应用上具有更大的灵活性．

Using weight factors, we obtain the Koppelman-Leray formula with weight fac- tors of (p,q) differential forms for a strictly pseudoconvex domain with not necessarily smooth boundaries on a complex manifold, and give an integral representation for the solu- tion with weight factors of -equation on this domain which does not involve integral on boundary, so we can avoid complex estimates of boundary integrals. Furthermore, with the introduction of weight factors, the integral formulas with weight factors have much freedom in application.