, Volume 249, Issue 1, pp 223-240

Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

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Abstract.

We show that maximal operators formed by dilations of Mikhlin- Hörmander 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.

Christ, Grafakos and Seeger were supported in part by NSF grants. Honzík was supported by 201/03/0931 Grant Agency of the Czech Republic