Issues related to Rubio de Francia’s Littlewood–Paley Inequality: A Survey
نویسنده
چکیده
Let Sωf = ∫ ω f̂(ξ)e ixξ dξ be the Fourier projection operator to an interval ω in the real line. Rubio de Francia’s Littlewood Paley inequality [31] states that for any collection of disjoint intervals Ω, we have ∥∥ [∑ ω∈Ω |Sωf | 1/2∥∥ p . ‖f‖p, 2 ≤ p <∞. We survey developments related to this inequality, including the higher dimensional case, and consequences for multipliers.
منابع مشابه
Issues related to Rubio de Francia’s Littlewood–Paley inequality
Let Sω f = ∫ ω f̂(ξ)e dξ be the Fourier projection operator to an interval ω in the real line. Rubio de Francia’s Littlewood–Paley inequality (Rubio de Francia, 1985) states that for any collection of disjoint intervals Ω, we have ∥∥∥∥ [∑ ω∈Ω |Sω f | 1/2∥∥∥∥ p ‖f‖p, 2 ≤ p < ∞. We survey developments related to this inequality, including the higher dimensional case, and consequences for multiplie...
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