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arXiv · 1501.07669

A characterization of maximal operators associated with radial Fourier multipliers

Jongchon Kim
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Abstract

We give a simple necessary and sufficient condition for maximal operators associated with radial Fourier multipliers to be bounded on $L^p_{rad}$ and $L^p$ for certain $p$ greater than $2$. The range of exponents obtained for the $L^p_{rad}$ 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.

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Jongchon Kim. 2016-08-30. A characterization of maximal operators associated with radial Fourier multipliers. https://arxiv.org/abs/1501.07669

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