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