# Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators

Preprint Series # 692
Terasawa, Yutaka Outer measures and weak type (1,1) estimates of Hardy-Littlewood maximal operators. (2004);

 TeX DVI51Kb

## Abstract

We will introduce the $k$ times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for $k>0$. We will prove the $k$ times modified centered Hardy-Littlewood maximal operator is weak type $(1,1)$ bounded with constant $1$ when $k \ge 2$ if the Radon measure of the space has continuitiy'' in some sense. In the proof, we will use the outer measure associated with the Radon measure. We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.

Item Type: Preprint 40 Hardy-Littlewood maximal operator, weak type $(1,1)$ estimate, operator norm, outer measure 42-xx FOURIER ANALYSIS 858