Issues related to Rubio de Francia's Littlewood--Paley Inequality: A Survey

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Rubio de Francia's Littlewood Paley inequality is an extension of the classical Littlewood Paley inequality to one that holds for a decomposition of frequency space into arbitrary disjoint intervals. We survey this inequality, its higher dimensional analogs, and the implications for multipliers.
43 pages, 43 references. Additional material and references added. A final polishing of the manuscript. To appear in NYJ Math

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