  The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de
Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach
lattice whose 2-concavification is a UMD Banach lattice has this property. The
paper also shows that every space having LPR_q also has LPR_p with q \leq p <
\infty.
