Maximal functions associated with Fourier multipliers of Mikhlin-H"ormander type
classification
🧮 math.CA
keywords
maximalmultipliersmikhlin-hoperatorsormanderassociatedboundedboundedness
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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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