This is an announcement for the paper "On the growth of vector-valued Fourier series" by Parcet Javier, Soria Fernando, and Xu Quanhua. Abstract: We prove the 'little Carleson theorem' on the growth of Fourier series for functions taking values in a UMD Banach space. Archive classification: math.CA math.FA Submitted from: javier.parcet@icmat.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.4313 or http://arXiv.org/abs/1109.4313