论文标题
用于强制pseudoconvex域的pluricomplex泊松内核
The pluricomplex Poisson kernel for strongly pseudoconvex domains
论文作者
论文摘要
在本文中，我们通过词句型定理介绍，这是强烈的假子共元域中的最大plurisubharmonic函数。我们将这样的功能称为{\ sl pluricomplex泊松内核}，因为它与单位光盘的经典泊松内核共享许多属性。特别是，我们表明这种函数是连续的，它在边界上为零，除了在一个边界点具有非区域简单极点并重现Pluriharmonic函数。我们还使用这样的函数来获得经典朱莉娅的引理和朱莉娅·沃尔夫 - 雅迪奥里派定理的新“内在”版本。
In this paper we introduce, via a Phragmen-Lindelöf type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {\sl pluricomplex Poisson kernel} because it shares many properties with the classical Poisson kernel of the unit disc. In particular, we show that such a function is continuous, it is zero on the boundary except at one boundary point where it has a non-tangential simple pole, and reproduces pluriharmonic functions. We also use such a function to obtain a new "intrinsic" version of the classical Julia's Lemma and Julia-Wolff-Carathéodory Theorem.
