In this paper we introduce, via a Phragmén-Lindelöf type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the 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's Theorem.

中文翻译：

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用于强伪凸域的pluricomplex Poisson核

在本文中，我们通过Phragmén-Lindelöf型定理介绍了强伪凸域中的最大次亚谐波函数。我们将此函数称为多复合泊松核，因为它与单位圆盘的经典泊松核具有许多特性。特别是，我们证明了这种函数是连续的，除了在一个具有非切向简单极点的边界点之外，该函数在边界处为零，并且可以再现多谐波函数。我们还使用此函数来获取经典Julia的引理和Julia-Wolff-Carathéodory定理的新“本征”版本。