Bergman spaces on disconnected domains
For a bounded open set $U$ in the complex plane, we consider the Bergman space $L^p_a(U)$ of $p$th-power area-integrable analytic functions on $U$, with $p$ assumed to be in the range $1\le p<+\infty$, where the lower bound assures that $L^p_a(U)$ is a Banach space. Fix a bounded domain $G$ and a compact subset $K$ of $G$ with zero area measure. Let $M$ be a closed subspace of $L^p_a(G\sbs K)$. We
