Interpolating Sequences for Weighted Bergman Spaces on Strongly Pseudoconvex Bounded Domains

TL;DR

This paper characterizes interpolating sequences for weighted Bergman spaces on strongly pseudoconvex domains, showing that separated sequences are exactly those that interpolate in certain parameter ranges.

Contribution

It provides a complete characterization of interpolating sequences for weighted Bergman spaces on strongly pseudoconvex domains under specific conditions.

Findings

Separated sequences are interpolating for the specified weighted Bergman spaces.

The characterization holds for certain ranges of p and β.

The results extend known interpolation criteria to more general 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 $A^p_\beta(\Omega)$. In the case, $1\leq p<\infty$, 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 $A^p_\beta(\mathbb{B}_n)$ if and only if it is separated.