Revista Matemática Iberoamericana


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Volume 28, Issue 3, 2012, pp. 839–856
DOI: 10.4171/RMI/693

Published online: 2012-07-16

On the vector-valued Littlewood–Paley–Rubio de Francia inequality

Denis Potapov[1], Fedor Sukochev[2] and Quanhua Xu[3]

(1) University of New South Wales, Sydney, Australia
(2) University of New South Wales, Sydney, Australia
(3) Wuhan University, Wuhan, Hubei, China

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 $q \leq p < \infty$.

Keywords: Littlewood–Paley–Rubio de Francia inequality, UMD space of type 2, Banach lattices

Potapov Denis, Sukochev Fedor, Xu Quanhua: On the vector-valued Littlewood–Paley–Rubio de Francia inequality. Rev. Mat. Iberoamericana 28 (2012), 839-856. doi: 10.4171/RMI/693