Interpolation by entire functions with growth conditions

Let $A_p(\C)$ be the space of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$ and let $V$ be a discrete sequence of complex numbers which is not a uniqueness set for $A_p(\C)$. We use $L^2$ estimates for the $\bar\partial$ equation to charaterize the trace of $A_p(\C)$ on $V$.