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

The Littlewood—Paley—Rubio de Francia property of a Banach space for the case of equal intervals