Interpolating Sequences for Weighted Bergman Spaces on Strongly Pseudoconvex Bounded Domains

Abstract

Let $0<p<\infty$, $\beta >-1$, and $\Omega$ be a strongly pseudoconvex bounded domain with a smooth boundary in ${\mathbb{C}}^n$. We will study the interpolation problem for weighted Bergman spaces $A_{\beta }^p(\Omega )$. In the case, $1\le p<\infty$, and $\beta >\max \{n(2p-1)-1,n(2q-1)-1\}$, 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 $A_{\beta }^p({\mathbb{B}}_n)$ if and only if it is separated.

14 pages, any comments/addition would be appreciated