composition operators between growth spaces on circular and strictly convex domains in complex banach spaces

Let ωx be a bounded, circular and strictly convex domain in a complex banach space x, and h(ωx) be the space of all holomorphic functions from ωx to c. the growth space a^ν (ωx) consists of all f ∈ h(ωx) such that |f(x)| ≤ cν(rωx (x)), x ∈ ωx, for some constant c > 0, whenever rωx is the minkowski functional on ωx and ν : [0, 1) → (0, ∞) is a nondecreasing, continuous and unbounded function. for complex banach spaces x and y and a holomorphic map φ : ωx → ωy , put cφ(f) = f ◦ φ, f ∈ h(ωy ). we characterize those φ for which the composition operator cφ : a ω (ωy ) → a^ν (ωx) is a bounded or compact operator.