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

Denis Potapov; Fedor Sukochev; Quanhua Xu

doi:10.4171/rmi/693

JournalsrmiVol. 28, No. 3pp. 839–856

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

Denis Potapov
University of New South Wales, Sydney, Australia
Fedor Sukochev
University of New South Wales, Sydney, Australia
Quanhua Xu
Wuhan University, Wuhan, Hubei, China

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Abstract

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 $q \leq p < \infty$ .

Cite this article

Denis Potapov, Fedor Sukochev, Quanhua Xu, On the vector-valued Littlewood–Paley–Rubio de Francia inequality. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 839–856

DOI 10.4171/RMI/693