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.
Information
Published: 1 January 2006
First available in Project Euclid: 16 December 2018
zbMATH: 1125.42008
MathSciNet: MR2279770
Digital Object Identifier: 10.2969/aspm/04410377
Subjects:
Primary:
31B15
,
42B25
Keywords:
Choquet integral
,
Hausdorff content
,
homogeneous space
,
maximal function
Rights: Copyright © 2006 Mathematical Society of Japan
