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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L_{p,\rho}^K(E)}$$\end{document} is isomorphic to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L_{p',\rho^{-1}}^{-K}(E')}$$\end{document} 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.