论文标题
伯格曼（Bergman
A uniqueness property for Bergman functions on the Siegel upper half-space
论文作者
论文摘要
In this paper, we show that the Bergman functions on the Siegel upper half-space enjoy the following uniqueness property: if $f\in A_t^p(\calU)$ and $\bfL^α f\equiv 0$ for some nonnegative multi-index $α$, then $f\equiv 0$, where $\bfL^α:=(\bfL_1)^{α_1} \ cdots（\ bfl_n）^{α_n} $，带有$ \ bfl_j = \ frac {\ partial} {\ partial z_j} + 2i \ 2i \ bar {z} _j \ frac {\ frac {\ partial} \ frac {\ partial} {\ partial z_n} $。结果，我们获得了伯格曼在西格尔上半个空间上的函数的新积分表示。最后，作为一个应用程序，我们得出了将伯格曼标准与“衍生范围”联系起来的结果，该结果暗示了Bloch空间的替代定义以及Siegel上半空间上BESOV空间的概念。
In this paper, we show that the Bergman functions on the Siegel upper half-space enjoy the following uniqueness property: if $f\in A_t^p(\calU)$ and $\bfL^α f\equiv 0$ for some nonnegative multi-index $α$, then $f\equiv 0$, where $\bfL^α:=(\bfL_1)^{α_1} \cdots (\bfL_n)^{α_n}$ with $\bfL_j = \frac{\partial }{\partial z_j} + 2i \bar{z}_j \frac{\partial }{\partial z_n}$ for $j=1,\ldots, n-1$ and $\bfL_n = \frac{\partial }{\partial z_n}$. As a consequence, we obtain a new integral representation for the Bergman functions on the Siegel upper half-space. In the end, as an application, we derive a result that relates the Bergman norm to a "derivative norm", which suggests an alternative definition of the Bloch space and a notion of the Besov spaces over the Siegel upper half-space.
