Abstract

In this paper we generalize the concept of the Szegö kernel by putting the weight of integration in the definition of the inner product in the Szegö space. We give some sufficient conditions for the weight in order for the Szegö kernel of the correspoding space to exist. We give examples of weights on unit ball for which there is no Szegö kernel of the corresponding Szegö space. Then using biholomorphisms we prove that there exist such weights for a large class of domains. At the end we show that weighted Szegö kernel depends continuously in some sense on weight of integration.

中文翻译：

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允许使用塞格尔型繁殖核的砝码

摘要

在本文中，我们通过将积分的权重放在Szegö空间中内积的定义中来概括Szegö内核的概念。我们给出一些足够的权重条件，以使相应空间的塞格核存在。我们给出单位球上没有对应Szegö空间的Szegö核的配重的示例。然后，使用双同构，我们证明了对于大类域都存在这样的权重。最后，我们表明加权的Szegö内核在某种意义上持续依赖积分的权重。