A characterization of maximal operators associated with radial Fourier multipliers

Abstract

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

Final version, 9 pages. Accepted for publication in Proceedings of the AMS

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