Geometric conditions for interpolation in weighted spaces of entire functions

We use $L^2$ estimates for the $\bar{\mathrm{\partial }}$ equation to find geometric conditions on discrete interpolating varieties for weighted spaces $A_p(\text{C})$ of entire functions such that $\mathrm{\mid }f(z)\mathrm{\mid }\le A{e}^{Bp(z)}$ for some $A,B>0$. In particular, we give a characterization when $p(z)=e^{\mathrm{\mid }z\mathrm{\mid }}$ and more generally when $\ln p(e^r)$ is convex and $\ln p(r)$ is concave.