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L h 2 -Functions in Unbounded Balanced Domains.
The Journal of Geometric Analysis ( IF 1.1 ) Pub Date : 2017-01-02 , DOI: 10.1007/s12220-016-9754-3
Peter Pflug 1 , Włodzimierz Zwonek 2
Affiliation  

We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a description of \(L_h^2\)-domains of holomorphy in the class of balanced domains and present a purely algebraic criterion for homogeneous polynomials to be square integrable in a pseudoconvex balanced domain in \(\mathbb {C}^2\). This allows easily to decide which pseudoconvex balanced domain in \(\mathbb {C}^2\) has a positive Bergman kernel and which admits the Bergman metric.

中文翻译:

L h 2-无界平衡域中的函数。

我们调查与(无界)平衡域上平方可积全纯函数的存在有关的问题。特别是,我们解决了维格在二维空间中的平衡域问题。我们还给出了平衡域类中全纯\(L_h ^ 2 \)-域的描述,并给出了齐次多项式在\(\ mathbb {C} ^ 2 \)。这使得可以轻松地确定\(\ mathbb {C} ^ 2 \)中的哪个伪凸平衡域具有正Bergman内核,以及哪个域承认Bergman度量。
更新日期:2017-01-02
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