Please use this identifier to cite or link to this item: https://doi.org/10.1002/mana.200310010
Title: Littlewood-Paley type inequality on ℝ
Authors: Quek, T.S. 
Keywords: Fourier multipliers
Singular integral operators
Weighted Lp-spaces
Issue Date: 2003
Citation: Quek, T.S. (2003). Littlewood-Paley type inequality on ℝ. Mathematische Nachrichten 248-249 : 151-157. ScholarBank@NUS Repository. https://doi.org/10.1002/mana.200310010
Abstract: Let {Ik}k∈ℕ be a sequence of well-distributed mutually disjoint intervals of ℝ\{0}. For f ∈ Lp(ℝ), 1 ≤ p ≤ 2, define SIkf by (SIkf)∧ = χIkikf̂ We prove that there exists a positive constant C such that
(Σk∈ℕ;|SIkf|p′)1/p′
p,p′ ≤ C
f
p for all f ∈ Lp(ℝ), 1 < p < 2, where 1/p + 1/p′ = 1 and
·
p,p′ is the norm of the Lorentz space Lp,p′ (ℝ). An application of our result to Fourier multipliers is given.
Source Title: Mathematische Nachrichten
URI: http://scholarbank.nus.edu.sg/handle/10635/103507
ISSN: 0025584X
DOI: 10.1002/mana.200310010
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