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

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.

preprint2004arXivOpen access
Michael ChristLoukas GrafakosPetr HonzikAndreas Seeger
math.CA
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Michael ChristLoukas GrafakosPetr HonzikAndreas Seeger

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