Maximal Marcinkiewicz multipliers

Petr Honzík Faculty of Mathematics and Physics, Charles University

Analysis of PDEs Functional Analysis mathscidoc:1701.03026

Arkiv for Matematik, 52, (1), 135-147, 2012.5
Let $\mathcal{M} =\{m_{j}\}_{j=1}^{\infty}$ be a family of Marcinkiewicz multipliers of sufficient uniform smoothness in $\mathbb{R}^{n}$ . We show that the$L$^{$p$}norm, 1<$p$<∞, of the related maximal operator $$M_Nf(x)= \sup_{1\leq j \leq N} |\mathcal{F}^{-1} ( m_j \mathcal{F} f)|(x) $$ is at most$C$(log($N$+2))^{$n$/2}. We show that this bound is sharp.
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@inproceedings{petr2012maximal,
  title={Maximal Marcinkiewicz multipliers},
  author={Petr Honzík},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637408769059},
  booktitle={Arkiv for Matematik},
  volume={52},
  number={1},
  pages={135-147},
  year={2012},
}
Petr Honzík. Maximal Marcinkiewicz multipliers. 2012. Vol. 52. In Arkiv for Matematik. pp.135-147. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203637408769059.
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