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.

Bracci, F., Saracco, A., Trapani, S. (2021). The pluricomplex Poisson kernel for strongly pseudoconvex domains. ADVANCES IN MATHEMATICS, 380 [10.1016/j.aim.2021.107577].

### The pluricomplex Poisson kernel for strongly pseudoconvex domains

#### Abstract

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.
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Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03
English
Con Impact Factor ISI
Pluripotential theory; pluricomplex Poisson kernel; holomorphic dynamics; strongly pseudoconvex domains
https://www.sciencedirect.com/science/article/abs/pii/S0001870821000153?via=ihub
Bracci, F., Saracco, A., Trapani, S. (2021). The pluricomplex Poisson kernel for strongly pseudoconvex domains. ADVANCES IN MATHEMATICS, 380 [10.1016/j.aim.2021.107577].
Bracci, F; Saracco, A; Trapani, S
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/289258`