Abstract
We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on L r a d p L^p_{rad} and L p L^p for certain p p greater than 2 2 . The range of exponents obtained for the L r a d p L^p_{rad} characterization is optimal for the given condition. The L p L^p characterization is derived from an inequality of Heo, Nazarov, and Seeger regarding a characterization of radial Fourier multipliers.
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