On maximal functions for Mikhlin-Hoermander multipliers

Loukas Grafakos; Petr Honzik; Andreas Seeger

On maximal functions for Mikhlin-Hoermander multipliers

经典分析与常微分方程 2010-03-15 v1

作者: Loukas Grafakos , Petr Honzik , Andreas Seeger

摘要

Given Mikhlin-H\"ormander multipliers $m_i$ , $i=1,..., N$ , with uniform estimates we prove an optimal $\sqrt{\log(N+1)}$ bound in $L^p$ for the maximal function $\sup_i|\cF^{-1}[m_i\hat f]|$ and related bounds for maximal functions generated by dilations.

关键词

maximal operators multiplier operators function spaces and inequalities

引用

@article{arxiv.math/0501114,
  title  = {On maximal functions for Mikhlin-Hoermander multipliers},
  author = {Loukas Grafakos and Petr Honzik and Andreas Seeger},
  journal= {arXiv preprint arXiv:math/0501114},
  year   = {2010}
}

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