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

Denis Potapov; Fedor Sukochev; Quanhua Xu

doi:10.4171/rmi/693

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

Denis Potapov^*
, Fedor Sukochev
, Quanhua Xu

^*Corresponding author for this work

University of New South Wales
Wuhan University
CNRS

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

The paper studies Banach spaces satisfying the Littlewood- Paley-Rubio de Francia property LPRp, 2 ≤ p < ∞. 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 also has LPRp with q ≤ p < ∞.

Original language	English
Pages (from-to)	839-856
Number of pages	18
Journal	Revista Matematica Iberoamericana
Volume	28
Issue number	3
DOIs	https://doi.org/10.4171/rmi/693
State	Published - 2012
Externally published	Yes

Keywords

Banach lattices
Littlewood-Paley-Rubio de Francia inequality
UMD space of type 2

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10.4171/rmi/693

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abstract = "The paper studies Banach spaces satisfying the Littlewood- Paley-Rubio de Francia property LPRp, 2 ≤ p < ∞. 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 also has LPRp with q ≤ p < ∞.",

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AB - The paper studies Banach spaces satisfying the Littlewood- Paley-Rubio de Francia property LPRp, 2 ≤ p < ∞. 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 also has LPRp with q ≤ p < ∞.

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KW - Littlewood-Paley-Rubio de Francia inequality

KW - UMD space of type 2

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M3 - 文章

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

Abstract

Keywords

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