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arXiv · 2007.06270

The pluricomplex Poisson kernel for strongly pseudoconvex domains

Filippo Bracci·Alberto Saracco·Stefano Trapani
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Abstract

In this paper we introduce, via a Phragmen-Lindel\"of 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-Carath\'eodory Theorem.

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Filippo Bracci, Alberto Saracco, Stefano Trapani. 2020-07-13. The pluricomplex Poisson kernel for strongly pseudoconvex domains. https://arxiv.org/abs/2007.06270

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