Estimates of maximal functions by Hausdorff contents in a metric space

Watanabe, Hisako

doi:10.2969/aspm/04410377

VOL. 44 | 2006 Estimates of maximal functions by Hausdorff contents in a metric space

Hisako Watanabe

Editor(s) Hiroaki Aikawa, Takashi Kumagai, Yoshihiro Mizuta, Noriaki Suzuki

Adv. Stud. Pure Math., 2006: 377-389 (2006) DOI: 10.2969/aspm/04410377

Abstract

Let $M$ be the Hardy-Littlewood maximal operator in a quasimetric space $X$. We give the estimates of $Mf$ with weak type and strong type with respect to the $\alpha$-Hausdorff content. To do these, we use the dyadic balls introduced by E. Sawyer and R. L. Wheeden.