Geometric conditions for interpolation in weighted spaces of entire functions

We use L-2 estimatesfor the partial derivative equation to find geometric conditions on discrete interpolating varieties for weighted spaces A(p)(C) of entire functions such that vertical bar f (z)vertical bar <= Ae(Bp(z)) for some A, B > 0. In particular, we give a characterization when p(z) = e(vertical bar z vertical bar) and more generally, when In p(e(r)) is convex and In p(r) is concave.