On weighted L p -spaces of vector-valued entire analytic functions

Abstract

The weighted Lp-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 χK is an Lp,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.