有界域上具有离散全纯核的Koppelman公式与-方程

Koppelman Formula with Discrete Holomorphic Kernel and ■-Equation on a Bounded Domain

D是Cn空间中具有逐块C(1)边界的有界域,该文建立了D上一个具有离散局部全纯核的 (0,q)形式的Koppelman积分公式及其相应的■-方程解的积分表示和它的内闭一致估计式.

Let D be a bounded domain with piecewise C(1) boundary in Cn,f∈C(0,q)(1)(D) and (?)f ∈C(0,q+1)(1)(D). The anthors establish a new integral formula of Koppelman of (0,q)-form with discrete holomorphic kernels on Dwhere L(?)Dηf,R(?)Dηf,BDf,R(?)Dη(?)f some corresponding integral operators. If (?)f = 0 , then u = (-1)q(R(?)Dη+BD)f is a local differentiabl solution of the equation (?)u=f in D, and u has an inner closed uniform estimate in D , i. e.||u||L∞≤C||f||L∞.