论文标题
莱因哈特域的加权繁殖核
The weighted reproducing kernels of the Reinhardt domain
论文作者
论文摘要
在本文中，我们开发了加权伯格曼空间的理论，并获得了包含起源的Reinhardt域上伯格曼内核函数的一般表示公式。作为应用程序，我们在Reinhardt域上计算一些特殊权重的混凝土形式$ \ Mathbb {C}^n，$ $ $ d_ {n，m}：= \ {（z，w）\ <{e}^{ - μ_1\ | z \ |^{μ_2}} \} $和$v_η：= \ {（z，z，z'，w）\ in \ in \ mathbb {c}^{c}^{n} \ times \ times \ times \ times \ times \ times \ mathbb {c}} \ sum_ {j = 1}^{n} e^{η_{J} | w |^{2}} | z__ {j} |^{2}+\ | z'\ |^{2} <1} <1 <1 \} $。
In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the concrete forms of the Bergman kernels for some special weights on the Reinhardt domains $\mathbb{C}^n,$ $D_{n,m}:= \{(z, w)\in \mathbb{C}^n \times \mathbb{C}^m : \|w\|^2 <{e}^{-μ_1\|z\|^{μ_2}}\}$ and $V_η:=\{(z, z', w) \in \mathbb{C}^{n} \times \mathbb{C}^{m} \times \mathbb{C} : \sum_{j=1}^{n} e^{η_{j}|w|^{2}}|z_{j}|^{2}+\|z'\|^{2}<1\}$.
