  Let $X$ be a Banach space. It is proved that an analogue of the Rubio de
Francia square function estimate for partial sums of the Fourier series of
$X$-valued functions holds true for all disjoint collections of subintervals of
the set of integers of equal length and for all exponents $p$ greater or equal
than 2 if and only if the space $X$ is a UMD space of type 2. The same
criterion is obtained for the case of subintervals of the real line and Fourier
integrals instead of Fourier series.
