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We use Oberlin, Nazarov, and Thiele's Multi-Frequency Calder\'{o}n-Zygmunddecomposition to lower estimates on maximal multipliers in $L^p$. We alsoimprove on classical multiplier results of Coifman, Rubio de Francia, andSemmes.

Some Optimizations for (Maximal) Multipliers in $L^p$