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

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

2003-11-28

arxiv.org/abs/math/0311538v3

Mathematische Zeitschrift, 249 (2005), 223-240.

Mathematics

Classical Analysis and ODEs

Final version with improved differentiability assumptions on the multipliers. To appear in Mathematische Zeitschrift

Scientific paper

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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