Issues related to Rubio de Francia’s Littlewood–Paley inequality
نویسنده
چکیده
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 multipliers. Mathematics Subject Classification. Primary: 42B25. Secondary: 42B30, 42B35.
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