On weighted Lp-spaces of vector-valued entire analytic functions

The weighted L-p-spaces of entire analytic functions are generalized to the vector-valued setting. In particular, it is shown that the dual of the space L-p,rho(K) (E) is isomorphic to L-p',rho-1(-K) (E') when the function chi (K) is an L (p,rho) (E)-Fourier multiplier. This result allows us to give some new characterizations of the so-called UMD-property and to represent several ultradistribution spaces by means of spaces of vector sequences.