一类Reinhardt域的Bergman核函数零点的边界性质

The Boundary Property of Zero Points of the Bergman Kernel Function on a Kind of Reinhardt Domains

本文研究了形如E_p={(ω,z)∈C^(1+n):|ω|^(2p)+‖z‖~2<1}p∈R^+的一类Reinhardt域,并针对非陆启铿域E_p探讨其Bergman核函数零点的边界性质,即给出了域E_p×E_p的不同类型边界的邻域内是否存在Bergman核函数零点的判别方法.

In this paper, we discuss a kind of Reinhardt domain： Ep={（w,z）∈C^1＋n：｜w｜^2p＋｜｜z｜｜^2〈1）,P∈R＋. As Ep is non Lu Qikeng domain, we analyze the boundary property of the zero point of the Bergman kernel function. That is to say, we discuss if there exists the zero point of Bergman kernel function in the neighborhood of （a, b） ∈δEp × δEp.