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Maximal functions associated with Fourier multipliers of Mikhlin-H"ormander type

Michael Christ·Loukas Grafakos·Petr Honzik·Andreas Seeger
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Abstract

We show that maximal operators formed by dilations of Mikhlin-H"ormander multipliers are typically not bounded on $L^p(R^d)$. We also give rather weak conditions in terms of the decay of such multipliers under which $L^p$ boundedness of the maximal operators holds.

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Michael Christ, Loukas Grafakos, Petr Honzik, Andreas Seeger. 2004-03-09. Maximal functions associated with Fourier multipliers of Mikhlin-H"ormander type. https://arxiv.org/abs/math/0311538

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