论文标题
加权伯格曼空间的插值序列在强pseudoconvex有限域上
Interpolating Sequences for Weighted Bergman Spaces on Strongly Pseudoconvex Bounded Domains
论文作者
论文摘要
令$ 0 <p <\ infty $，$β> -1 $，而$ω$是一个强烈的pseudoconvex有限域，在$ \ mathbb {c}^n $中具有光滑边界。我们将研究加权伯格曼空间$ a^p_β（ω）$的插值问题。在这种情况下，$ 1 \ leq p <\ infty $和$β> \ max \ {n（2p-1）-1，n（2q-1）-1 \} $，其中$ q $是$ p $的共轭指数（$ q = 1 $，对于$ p = 1 $） $ \ mathbb {c}^n $，以$ a^p_β（\ mathbb {b} _n）$进行插值，仅当它分开时。
Let $0<p<\infty$, $β>-1$, and $Ω$ be a strongly pseudoconvex bounded domain with a smooth boundary in $\mathbb{C}^n$. We will study the interpolation problem for weighted Bergman spaces $A^p_β(Ω)$. In the case, $1\leq p<\infty$, and $β> \max \{n(2p-1)-1, n(2q-1)-1\}$, where $q$ is the conjugate exponent of $p$ (let $q=1$, for $p=1$), we show that a sequence in $\mathbb{B}_n$, the unit ball in $\mathbb{C}^n$, is interpolating for $A^p_β(\mathbb{B}_n)$ if and only if it is separated.
