2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67918Rubio 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 MathClassical Analysis and ODEs42text