Rubio de Francia’s Littlewood-Paley inequality for operator-valued functions
نویسندگان
چکیده
We prove Rubio de Francia’s Littlewood-Paley inequality for arbitrary disjoint intervals in the noncommutative setting, i.e. for functions with values in noncommutative L-spaces. As applications, we get sufficient conditions in terms of q-variation for the boundedness of Schur multipliers on Schatten classes.
منابع مشابه
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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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