OPERATORS ON FOCK-TYPE AND WEIGHTED SPACES OF ENTIRE FUNCTIONS

Let us denote by F-1(phi)(C) the space of entire functions f is an element of H(C) such that integral(C)vertical bar f(z)vertical bar e(-phi(vertical bar z vertical bar)) dm(z) < infinity where phi : ( 0, infinity) -> R+ is assumed to be continuous and non- decreasing. Also given a continuous non-increasing function v : (0, infinity) -> R+ and a complex Banach space X, we write H-v(infinity)(C, X) for the space of X-valued entire functions F such that sup(z is an element of C) v(z)parallel to F(z)parallel to < infinity. We find a very general class of weights phi and v for which the space of bounded operators L(F-1(phi)(C), X) can be identified with H-v(infinity) (C, X).