论文标题
单一地图下的伯格曼空间
Bergman spaces under maps of monomial type
论文作者
论文摘要
对于适当的域$ω__{1}，ω_{2} $，我们考虑映射$φ_{\ Mathbf a}：ω__{1} \ to tomomial类型的$。我们将Bergman Space $ \ Mathcal a^{2}（ω_{1}）$的正交分解成有限的许多封闭子空间，该子空间由与映射$φ_{\ MathBf a} $相关的有限ABELIAN组的字符索引。然后，我们证明每个子空间都是$ω_{2} $的加权伯格曼空间的同构。这导致$ω_{1} $作为$ω__________________________________________________________________________________________________________________________________________________________________________________________________________{}上
For appropriate domains $Ω_{1}, Ω_{2}$ we consider mappings $Φ_{\mathbf A}:Ω_{1}\toΩ_{2}$ of monomial type. We obtain an orthogonal decomposition of the Bergman space $\mathcal A^{2}(Ω_{1})$ into finitely many closed subspaces indexed by characters of a finite Abelian group associated to the mapping $Φ_{\mathbf A}$. We then show that each subspace is isomorphic to a weighted Bergman space on $Ω_{2}$. This leads to a formula for the Bergman kernel on $Ω_{1}$ as a sum of weighted Bergman kernels on $Ω_{2}$
