Maximal functions associated with Fourier multipliers of Mikhlin-Hörmander type

@article{Christ2003MaximalFA,
title={Maximal functions associated with Fourier multipliers of Mikhlin-H{\"o}rmander type},
author={Michael Christ and Loukas Grafakos and Petr Honz{\'i}k and Andreas Seeger},
journal={Mathematische Zeitschrift},
year={2003},
volume={249},
pages={223-240}
}
• Published 28 November 2003
• Mathematics
• Mathematische Zeitschrift
Abstract.We show that maximal operators formed by dilations of Mikhlin- Hörmander multipliers are typically not bounded on Lp(ℝd). We also give rather weak conditions in terms of the decay of such multipliers under which Lp boundedness of the maximal operators holds.
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References

SHOWING 1-10 OF 14 REFERENCES

Demonstration d'une version du theoreme des multiplicateurs de Hormander. Etude de quelques operateurs maximaux
Prolegomena. 1. L p Spaces and Interpolation. 2. Maximal Functions, Fourier Transform, and Distributions. 3. Fourier Analysis on the Torus. 4. Singular Integrals of Convolution Type. 5.