Maximal functions associated with Fourier multipliers of Mikhlin-H"ormander type
Classical Analysis and ODEs
2010-03-15 v3
Abstract
We show that maximal operators formed by dilations of Mikhlin-H"ormander multipliers are typically not bounded on . We also give rather weak conditions in terms of the decay of such multipliers under which boundedness of the maximal operators holds.
Cite
@article{arxiv.math/0311538,
title = {Maximal functions associated with Fourier multipliers of Mikhlin-H"ormander type},
author = {Michael Christ and Loukas Grafakos and Petr Honzik and Andreas Seeger},
journal= {arXiv preprint arXiv:math/0311538},
year = {2010}
}
Comments
Final version with improved differentiability assumptions on the multipliers. To appear in Mathematische Zeitschrift