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

Abstract

The paper studies Banach spaces satisfying the Littlewood–Paley–Rubio de Francia property LPRp_p, 2p<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 LPRq_q also has LPRp_p with qp<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