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Littlewood–Paley type inequality on ℝ

✍ Scribed by Tong Seng Quek

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
152 KB
Volume
248-249
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let {I~k~}~k∈ℕ~ be a sequence of well–distributed mutually disjoint intervals of ℝ{0}. For f ∈ L^p^(ℝ), 1 ≤ p ≤ 2, define S____f by (S____f)ˆ = χ$\hat f $. We prove that there exists a positive constant C such that

for all f ∈ L^p^(ℝ), 1 < p < 2, where 1/p + 1/p′ = 1 and ‖ · ‖~p,p′~ is the norm of the Lorentz space L^p,p′^ (ℝ). An application of our result to Fourier multipliers is given.

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