On weighted L p -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 is isomorphic to when the function χ _K is an L _p,ρ (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. J. Motos is partially supported by DGI (Spain), Grant BFM 2002-04013 and Grant MTEM 2005-08350-C03-03.