An operator representation for weighted spaces of vector valued holomorphic functions

For any weighted space HV(G) of holomorphic functions on an open set G ? ?^Nwith a topology stronger than that of uniform convergence on the compact sets and for any quasibarrelled space E we prove the topological isomorphism $HV(G,E_{b}^{\prime})={\cal L}_b(E,HV(G))$ and derive a similar, more complicated isomorphism for weighted spaces of continuous functions. This generalizes results of 3], 7] and 6] and should be compared with the ∈-product representations for the corresponding spaces of functions with o-growth conditions. At the end we also show the topological isomorphism HV₁(G₁, HV₂(G₂)) = H (V₁ ? V₂)(G₁ × G₂).