Interpolating sequences for the Bergman space and the $\bar\partial$-equation in weighted $L^p$

Abstract

The author showed that a sequence in the unit disk is a zero sequence for the Bergman space $A^p$ if and only if a certain weighted space $L^p(W}$ contains a nontrivial analytic function. In this paper it is shown that the sequence is an interpolating sequence for $A^p$ if and only if it is separated in the hyperbolic metric and the $\bar\partial$-equation $(1 - |z|^2)\bar\partial u = f$ has a solution $u$ belonging to $L^p(W)$ for every $f$ in $L^p(W)$.