English

On maximal functions for Mikhlin-Hoermander multipliers

Classical Analysis and ODEs 2010-03-15 v1

Abstract

Given Mikhlin-H\"ormander multipliers mim_i, i=1,...,Ni=1,..., N, with uniform estimates we prove an optimal log(N+1)\sqrt{\log(N+1)} bound in LpL^p for the maximal function supi\cF1[mif^]\sup_i|\cF^{-1}[m_i\hat f]| and related bounds for maximal functions generated by dilations.

Keywords

Cite

@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}
}